The discrete variable–finite basis approach to quantum scattering

We study theoretically the ground and excited bound states of the bosonic rare gas van der Waals trimer Ne(3). A slow variable discretization approach is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved using basis splines at a series of fixed finite-element methods discrete variable representation hyper-radii. We consider not only zero total nuclear orbital angular momentum, J = 0, states but also J > 0 states. By using the best empirical neon dimer interaction potentials, all the bound state energy levels of Ne(3) will be calculated for total angular momenta up to J = 6, as well as their average root-mean-square radii. We also analyze the wave functions in hyperspherical coordinates for several selected bound states.

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach

Suno

2011

“…͑11͒ requires the evaluation of the basis functions on a grid of N R ϫ N r ϫ N points by transformation methods. A fast sine transform 43,44 is applied along R, a symmetrized Legendre transformation 45 is used along , and a potential optimized ͑PO͒ transformation is defined by diagonalizing the r operator 46,47 in the v ͑r͒ vibrational basis.…”

Section: A Methodsmentioning

confidence: 99%

Ab initio vibrational predissociation dynamics of He–I2(B) complex

Valdés

Prosmiti

Villarreal

et al. 2007

Three-dimensional quantum mechanical calculations on the vibrational predissociation dynamics of HeI 2 B state complex are performed using a potential energy surface accurately fitted to unrestricted open-shell coupled cluster ab initio data, further enabling extrapolation for large I 2 bond lengths. A Lanczos iterative method with an optimized complex absorbing potential is used to determine energies and lifetimes of the vibrationally predissociating He, I 2 ͑B , vЈ͒ complex for vЈ ഛ 26 of I 2 vibrational excitations. The calculated predissociating state energies agree with recent experimental results within 0.5 cm −1 . This excellent agreement is remarkable since no adjustment was made with respect to the experiments. The present ab initio approach, however, shows its limitations in the fact that the computed lifetimes that are highly sensitive to subtle details of the potential energy surfaces such as anisotropy, are a factor of 1.5 larger than the available experimental data.

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] To calculate rovibrational spectra, rate constants, photodissociation cross sections, etc., one must calculate matrix elements either of the Hamiltonian or of factors of terms of the Hamiltonian. The DVR simplifies computing matrix elements because if DVR basis functions are used there is no need to do numerical quadratures.…”

Section: Introductionmentioning

confidence: 99%

A multidimensional discrete variable representation basis obtained by simultaneous diagonalization

Dawes

Carrington

2004

Direct product basis functions are frequently used in quantum dynamics calculations, but they are poor in the sense that many such functions are required to converge a spectrum, compute a rate constant, etc. Much better, contracted, basis functions, that account for coupling between coordinates, can be obtained by diagonalizing reduced dimension Hamiltonians. If a direct product basis is used, it is advantageous to use discrete variable representation (DVR) basis functions because matrix representations of functions of coordinates are diagonal in the DVR. By diagonalizing matrices representing coordinates it is straightforward to obtain the DVR that corresponds to any direct product basis. Because contracted basis functions are eigenfunctions of reduced dimension Hamiltonians that include coupling terms they are not direct product functions. The advantages of contracted basis functions and the advantages of the DVR therefore appear to be mutually exclusive. A DVR that corresponds to contracted functions is unknown. In this paper we propose such a DVR. It spans the same space as a contracted basis, but in it matrix representations of coordinates are diagonal. The DVR basis functions are chosen to achieve maximal diagonality of coordinate matrices. We assess the accuracy of this DVR by applying it to model four-dimensional problems.