Imaginary-Time Time-Dependent Density Functional Calculation of Excited States of Atoms Using CWDVR Approach

We have calculated the energies of excited states for the He, Li, and Be atoms by the time dependent self-consistent Kohn Sham equation using the Coulomb Wave Function Discrete Variable Representation CWDVR) approach. The CWDVR approach was used the uniform and optimal spatial grid discretization to the solution of the Kohn-Sham equation for the excited states of atoms. Our results suggest that the CWDVR approach is an efficient and precise solutions of excited-state energies of atoms. We have shown that the calculated electronic energies of excited states for the He, Li, and Be atoms agree with the other researcher values.

Charmonium Properties Using the Discrete Variable Representation (DVR) Method

The Schrödinger equation is solved numerically for charmonium using the discrete variable representation (DVR) method. The Hamiltonian matrix is constructed and diagonalized to obtain the eigenvalues and eigenfunctions. Using these eigenvalues and eigenfunctions, spectra and various decay widths are calculated. The obtained results are in good agreement with other numerical methods and with experiments.

Beyond Born-Oppenheimer Based Diabatic Surfaces of 1,3,5-C6H3F3+ to Generate the Photoelectron Spectra Using Time-Dependent Discrete Variable Representation Approach

In this article, Beyond Born-Oppenheimer (BBO) treatment is implemented to construct diabatic potential energy surfaces (PESs) of 1,3,5-C6H3F3+ over a series [eighteen (18)] of two-dimensional (2D) nuclear planes constituted with...

Determinação de Constantes Espectroscópicas Rovibracionais via Monte Carlo Quântico

This work evaluated the efficiency of the Diffusion quantum Monte Carlo (DMC) method in determining potential energy curves (PECs) for diatomic systems. This evaluation was performed by determining rovibrational spectroscopic constants from PECs obtained for the HeH+ and LiH systems. The trial wave functions used are derived from the Hartree-Fock and MCSCF methods. The method used to calculate the spectroscopic constants was the Discrete Variable Representation (DVR) method. Thus, the PECs generated from the DMC produced the best results, being very close to the experimental results. Thus, the DMC method proved to be more efficient than the other methods used (MCSCF and CCSD(T)). The results obtained in this study indicate that the DMC-DVR methodology has a great potential to become a reference in the determination of spectroscopic properties.

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.