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Techniques of Chiroptical Spectroscopy
Published in Grinberg Nelu, Rodriguez Sonia, Ewing’s Analytical Instrumentation Handbook, Fourth Edition, 2019
Nelu Grinberg, Harry G. Brittain, Sonia Rodriguez
Most forms of optical spectroscopy are usually concerned with measurement of the absorption or emission of electromagnetic radiation, the energy of which lies between 10 and 50,000 wavenumbers. Any possible effects associated with the polarization of the electric vectors of the radiant energy are not normally considered during the course of commonly performed experiments. For molecules lacking certain types of molecular symmetry, interactions with polarized radiation are important and can be utilized to study a wide variety of phenomena. Materials are therefore classified as being either isotropic (incapable of influencing the polarization state of light) or anisotropic (having the ability to affect the polarization properties of transmitted light).
A kinetic model and parameters estimate for the synthesis of 2-phenyloctane: a starting material of bio-degradable surfactant
Published in Indian Chemical Engineer, 2023
Sudip Banerjee, Md Aurangzeb, Amit Kumar
The above-mentioned research for the kinetic model development does not consider the symmetry change between the reactant and activated complex. However, according to Pearson [18], there is a change in the energy of the orbital of atoms due to the difference in the relative position of the atom during the chemical reaction. In this context, the molecular symmetry provided by group theory is helpful to study the molecular orbitals because it leads to a smooth response from reactants to products. It is interesting to know that the open literature has extensively used the concept of single-event to develop the kinetic model for processes, such as catalytic cracking of vacuum gas oil, methanol to olefin transformation, iso-butane alkylation with butane and paraffin hydrocracking and hydroisomerisation [19–22]. Therefore, considering the importance of molecular symmetry, this work proposes a kinetic model that considers the concept of symmetry (or single-event). At the same time, contrary to the previous work, we have assumed an unequal kinetic rate constant associated with the protonation of 1-octene and alkylation for the formation of 2-phenyloctane and its isomers.
A simplified Bixon–Jortner–Plotnikov method for fast calculation of radiationless transfer rates in symmetric molecules
Published in Molecular Physics, 2023
A. I. Martynov, A. S. Belov, V. K. Nevolin
Pekar has expressed the density of states as the function below [33]: where , , are effective parameters gotten for an infinite crystal, is the second approximation of the time correlated function , is the averaged frequency of all vibronic modes of the molecule, is the local extreme point on the complex plane, z is an integer running from to , is the Huang-Rhys factor (HRF). The formula (5) approximately determines the extreme point of if all vibronic frequencies are close to . To find the density of states, one needs to sum all terms with even z, when condition is met. According to Pekar, formula (4) does not give an insight into the spectrum, so an approximation (10) using a Gaussian function [33,34] was derived. Lax discovered a similar formula independently of Pekar [35]. The formula (10) can describe processes of excitation and de-excitation, depending on the sign before the Stokes shift . The plus sign stands for excitation processes while the minus sign is for de-excitation. The formula (10) is more illustrative than (4), but it only works in the region of the maximal density of states. Molecular symmetry usually makes it possible to simplify calculations. Despite this fact, its influence on the conversion rate remains relatively poorly known. Toniolo and Persico [31] made an attempt to study the role of symmetry in the Dushinsky effect. As a result, they found that calculation of rates can be simplified by converting the mode coefficient matrix into a block-diagonal form. According to Li et al. [36], one can get more information about a system, if the rate within the BJP framework is expressed via normal coordinates. Authors stated that the displacement along normal coordinate is zero for non-totally symmetric modes. They also expressed non-adiabatic coupling constants using derivatives with respect to normal coordinates. where is the wave function of the ath state, is the wave function of the bth state, is the normal coordinate of the pth mode.