Related papers: A symmetry-adapted algebraic approach to molecular…
The highly excited stretching vibrational energy levels and the intensities of infrared transitions in tetrahedral molecules are studied in a U(2) algebraic model. Its applications to silane and silicon tetrafluoride are presented with…
We introduce an accurate and efficient algebraic technique for the computation of the vibrational spectra of triatomic molecules, of both linear and bent equilibrium geometry. The full three-dimensional potential energy surface (PES), which…
We discuss semiempirical approaches and parametric methods developed for modeling molecular vibronic spectra. These methods, together with databases of molecular fragments, have proved efficient and flexible for solving various problems…
We present a general, numerically motivated approach to the construction of symmetry adapted basis functions for solving ro-vibrational Schr\"{o}dinger equations. The approach is based on the property of the Hamiltonian operator to commute…
The relation between algebraic and traditional calculations of molecular vibrations is investigated. An explicit connection between interactions in configuration space and the corresponding algebraic interactions is established.
The vibrational behavior of molecules serves as a crucial fingerprint of their structure, chemical state, and surrounding environment. Neutron vibrational spectroscopy provides comprehensive measurements of vibrational modes without…
An algebraic model of Boson-realization is proposed to study the vibrational spectra of a tetrahedral molecule, where ten sets of boson creation and annihilation operators are used to construct the Hamiltonian with $T_{d}$ symmetry. There…
This paper addresses the three following questions. (i) How the structures of group and of chain of groups enter nuclear, atomic and molecular spectroscopy? (ii) How these structures can be exploited, in a quantum- mechanical framework, in…
Explicit algebraic expressions for the expansion of the vibrational matrix elements in series of matrix elements on the wave functions of the ground vibrational state have been obtained for arbitrary sufficiently differentiable functions of…
We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential…
Vibrational spectroscopy is a key technique to elucidate microscopic structure and dynamics. Without the aid of theoretical approaches, it is however, often difficult to understand such spectra at a microscopic level. Ab initio molecular…
We propose a method, based on a Generalized Heisenberg Algebra (GHA), to reproduce the anharmonic spectrum of diatomic molecules. The theoretical spectrum generated by GHA allows us to fit the experimental data and to obtain the…
This work presents the first steps to modelling synthetic rovibrational spectra for all molecules of astrophysical interest using a new approach implemented in the Prometheus code. The goal is to create a new comprehensive source of…
We present Symphony, an $E(3)$-equivariant autoregressive generative model for 3D molecular geometries that iteratively builds a molecule from molecular fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for…
A framework to calculate two-particle matrix elements for fully antisymmetrized three-cluster configurations is presented. The theory is developed for a scattering situation described in terms of the Algebraic Model. This means that the…
The algebraic molecular model is used in $^{12}$C to construct densities and transition densities connecting low-lying states of the rotovibrational spectrum, first and foremost those belonging to the rotational bands based on the ground…
Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A…
The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic…
We present systematic comparison of three quantum mechanical approaches describing excitation dynamics in molecular complexes using the Time-Dependent variational principle (TDVP) with three increasing sophistication trial wavefunctions…
A new method is introduced to study three-body clusters. Triangular configurations with ${\cal D}_{3h}$ point-group symmetry are analyzed. The spectrum, transition form factors and $B(E\lambda)$ values of $^{12}$C are investigated. It is…