We have introduced an algebraic technique to biomolecules (porphyrins) family to determine the vibrational spectra. We present an algebraic model of vibrations of polyatomic biomolecules, as an example, the vibrational analysis of stretching modes of nickel octaetheylporphyrin (Ni(OEP)) and its isotopomers. The algebraic technique obtained the results are compared with experimental data; the results are showing good accuracy. Some reassignments of energy levels that predict location of energy states not yet observed. 1. Introduction For the last few years, theoretical studies of highly excited vibrational states of polyatomic molecules have been one of the most interesting topics for theoreticians and experimentalists because of the development of new laser spectroscopic techniques. The measurements of highly-excited overtone-combination spectra of molecules have renewed in a theoretical description and understanding of the observed spectral properties. Two approaches have mostly been used so far in an analysis of experimental data: (1) the familiar Dunham-like expansion of energy levels in terms of rotations-vibrations quantum numbers and (2) the solution of Schrodinger equation with potentials obtained either by appropriately modifying ab initio calculations or by more phenomenological methods. In this paper, we begin a systematic analysis of overtone-combination spectra and intensities of molecules in terms of novel approach: (3) vibron model [1–4]. An algebraic model of boson realization is proposed to study the vibrational spectra of a tetrahedral molecule [5]. The analytical expression for the vibrational transition probability is obtained by using an algebraic approach [6]. We study the dynamical entanglement of vibrations in small molecules by employing algebraic models [7]. This model is a formulation of the molecular spectral problem in terms of elements of Lie algebra, and it contains the same physical information of the Dunham and potential approach. However, by making use of the powerful methods of group theory, one is able to obtain the desired results in a much faster and straightforward way. Potential energy surfaces also play an important role in studying theoretical chemistry. The expression of the potential energy surface containing information about the bending motion of triatomic molecules is derived by using the semiclassical limit of the algebraic Hamiltonian with the dynamical symmetry group [8, 9]. In recent years, these polyatomic biomolecules (i.e., metalloporphyrins) have huge importance in the field of chemical physics. In
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