Vectors and eigenvalues when calculating the dipole strength
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BÎCLEA, Diana. Vectors and eigenvalues when calculating the dipole strength. In: Conference on Applied and Industrial Mathematics: CAIM 2022, Ed. 29, 25-27 august 2022, Chişinău. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2022, Ediţia a 29, pp. 82-84. ISBN 978-9975-81-074-6.
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Conference on Applied and Industrial Mathematics
Ediţia a 29, 2022
Conferința "Conference on Applied and Industrial Mathematics"
29, Chişinău, Moldova, 25-27 august 2022

Vectors and eigenvalues when calculating the dipole strength


Pag. 82-84

Bîclea Diana
 
Lucian Blaga University Sibiu
 
 
Disponibil în IBN: 20 decembrie 2022


Rezumat

This work is centered on some results obtained based on studies done on papers [4]. The ref. [4] describes the idea that when studying the vibration modes of molecules with infrared intensities (IR) only three intensities are used, as described by three eigenvectors, because the others are zero. We are interested in determining the vectors and eigenvalues of a matrix according to the scheme in the paper [4] only for VCD (vibrational circular dichroism) technology and to establish a link between vectors, eigenvalues and dipole strength. We will denote by ⃗μE = [⃗E 01(i)]β (EDTM -electric dipole transition moments) associated with the fundamental transition |0 >−→ |1 > of the ith vibrational mode, where β are the Cartesian coordinates for atoms, i = 1, 3N are vibrational mode. Let the matrix: Mpq = 3 k=1 ∂⃗μk ∂Qp ∂⃗μk ∂Qq , (1)where ∂⃗μk ∂Qp is the k−th component of the dipole derivative (of massweighted) with respect to normal coordinate Qp, 1 ≤ p, q ≤ N. Figure 6. The molecule of 1,3-dichloroallene, 7 atoms We diagonalize the matrix M from eq. (1) we will obtain only three non-zero values, so that we can study the vibration modes only according to the vectors corresponding to the eigenvalue. A connection was also established between the eigenvectors corresponding to tj eingenvectors Tj and the dipole strengh (D01) (Fig.1). 3N i=1 D01(i) = 3N j=1 tjT2 j . (2) The above study makes it possible to study the spectra and vibrations of molecules not only with experimental technologies but also studying with technologies of computational physics based on vibrational circular dichroism (VCD).