ALGEBRAIC APPROACH FOR AN ACCURATE SIMULATION OF CO2 RAMAN SPECTRA

We present an accurate simulation of the Raman spectrum of the carbon dioxide molecule in the 1150--1500~cm$^{-1}$ spectral range, comparing the results obtained using different polyad schemes. We first determine an optimal set of Hamiltonian interactions for the three different polyad schemes to after fit the 178 experimental term energies found in the literature. Thereafter, using a Taylor series expansion of the mean polarizability in terms of normal mode coordinates, we perform an additional canonical transformation followed by an anharmonization procedure and a fit to a subset of experimental transition moments. Once these steps are accomplished, the Raman spectrum of CO$_2$ is simulated and compared with the experiment

An algebraic alternative for the accurate simulation of CO2 Raman spectra

We present an accurate simulation of the Raman spectrum of the carbon dioxide molecule in the 1150–1500 cm−1 spectral range, comparing the results obtained using the three polyad schemes found in the literature of this molecule. The description of the molecule with the algebraic U1(2) × U(3) × U2(2) local model encompasses both stretching and bending degrees of freedom. A detailed analysis of the Hamiltonian interactions for the three polyad schemes provides fittings with root mean square deviations in the range 0.14–0.20 cm−1, involving 19 parameters taking into account the 178 experimental term energies found in the literature. Using a limited subset of 9 experimental transitionmoments, we optimize 5 partial derivatives of the mean polarizability and simulate the Raman spectrum of CO2 for the three polyad schemes. Comparing the calculated results with the experimental spectrum, we obtain an overall good agreement for the three polyads. However, an inspection in detail of the spectrum seems to show a slight preference for polyad P212 albeit not due to the interaction characterizing the polyad but due to anharmonic effects and energy distribution. Finally, we assess the effect of the Fermi resonance over CO2 Raman line intensities.Centro de Estudios Avanzados de Física, Matemática y Computación. Universidad de Huelva, Grant/Award Number: FEDER/MINECO UNHU-15CE-28; CMST COST action, Grant/Award Number: CM1405 MOLIM; Consejería de Conocimiento. Investigación y Universidad, Junta de Andalucía and European Regional Development Fund, Grant/Award Number: SOMM17/6105/UGR; Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México, Grant/Award Number: IN-22701

Algebraic DVR Approaches Applied to Describe the Stark Effect

Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the operators r2 and p2 are diagonalized to define useful bases to obtain the matrix representation of the Hamiltonian in a simple form in terms of diagonal matrices. The second approach is based on the U(4) dynamical algebra which consists of the addition of a scalar boson to the 3D harmonic oscillator space keeping constant the total number of bosons. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations, whose involved branching rules define the discrete variable representation. Both methods, although originating from the harmonic oscillator basis, provide different convergence tests due to the fact that the associated discrete bases turn out to be different. These approaches provide powerful tools to obtain the matrix representation of 3D general Hamiltonians in a simple form. In particular, the Hydrogen atom interacting with a static electric field is described. To accomplish this task, the diagonalization of the exact matrix representation of the Hamiltonian is carried out. Particular attention is paid to the subspaces associated with the quantum numbers n=2,3 with m=0

Algebraic vibrational description of the symmetric isotopologues of CO2: (13)C(16)O2 , (12)C(18)O2 and (12)C(17)O2

We present a polyad-conserving local model applied to the vibrational excitations of symmetric isotopologues of carbon dioxide. The description is carried out in the framework of local internal coordinates where the stretching degrees of freedom are modeled with Morse oscillators while for the bending modes the algebraic model is introduced. Three isotopologues are considered, namely O2, O2 and O2 in their electronic ground states. In all cases the most extensive experimental dataset of vibrational energies were taken into account. For the three isotopologues a Hamiltonian with interactions up to sixth order involving 16 parameters was considered. The description of the isotopologue O2 involved 110 experimental energies with a rms = 0.06 cm−1. On the other hand, for the isotopologue O2, only 42 experimental energies were available and a rms = 0.05 cm−1 was obtained with 15 parameters. For the isotopologue O2, considering 28 experimental energy terms a rms = 0.17 cm−1 was obtained. In addition, as a consequence of the normal mode behavior of these molecules, alternative polyad schemes were explored.This work is partially supported by DGAPA-UNAM, Mexico, under project IN-212020. M.C. acknowledges the financial support from the European Union’s Horizon 2020 research and innovation program under the Marie Sk lodowska-Curie grant agreement No 872081; from the Spanish National Research, Development, and Innovation plan (RDI plan) under the project PID2019-104002GB-C21; the Consejer´ıa de Conocimiento, Investigaci´on y Universidad, Junta de Andaluc´ıa and European Regional Development Fund (ERDF), ref. SOMM17/6105/UGR; and the Ministerio de Ciencia, Innovaci´on y Universidades (ref.COOPB20364)

Algebraic DVR Approaches Applied to Describe the Stark Effect

Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the operators r 2 and p 2 are diagonalized to define useful bases to obtain the matrix representation of the Hamiltonian in a simple form in terms of diagonal matrices. The second approach is based on the U(4) dynamical algebra which consists of the addition of a scalar boson to the 3D harmonic oscillator space keeping constant the total number of bosons. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations, whose involved branching rules define the discrete variable representation. Both methods, although originating from the harmonic oscillator basis, provide different convergence tests due to the fact that the associated discrete bases turn out to be different. These approaches provide powerful tools to obtain the matrix representation of 3D general Hamiltonians in a simple form. In particular, the Hydrogen atom interacting with a static electric field is described. To accomplish this task, the diagonalization of the exact matrix representation of the Hamiltonian is carried out. Particular attention is paid to the subspaces associated with the quantum numbers n = 2, 3 with m = 0.DGAPA-UNAM, IN-212020Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía FQM-160Ministerio de Ciencia e Innovación, FIS2017-88410-P, RTI2018-098117-B-C21, PID2019-104002GB-C22European Commission, H2020-INFRAIA-2014-201