An improved Lobatto discrete variable representation by a phase optimisation and variable mapping method

Yu, Dingfeng; Cong, Shu‐Lin

doi:10.1016/j.chemphys.2015.07.009

Cited by 6 publications

(2 citation statements)

References 70 publications

(98 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This fact not only leads to low grid efficiency but also makes the iterative propagator, such as short-time iterative Lanczos (SIL) method, converge slowly [23]. To overcome this difficulty, one can use the variable mapping method or prolate spheroidal wave functions to get a more uniform spatial grid far from the origin and dense spatial grid around the origin, to increase the numerical efficiency [24,25]. In the bottom panels of Figure 2, the gird distribution becomes nearly even after optimization, which improves the efficiency of the grid.…”

Section: Multidomain Spectral Element Methodsmentioning

confidence: 99%

Electronic and Molecular Dynamics by the Quantum Wave Packet Method

Sun

2016

Research Advances in Quantum Dynamics

Self Cite

View full text Add to dashboard Cite

A solution to the time-dependent Schrödinger equation is required in a variety of problems in physics and chemistry. In this chapter, recent developments of numerical and theoretical techniques for quantum wave packet methods efficiently describe the dynamics of molecular dynamics, and electronic dynamics induced by ultrashort laser pulses in atoms and molecules will be reviewed, particularly on the development of grid methods and time-propagation or pseudo-time evolution methods developed recently. Applications of the quantum wave packet for studying the reactive resonances in F + H 2 /HD and O + O 2 reaction, dissociative chemisorption of water on transitionmetal surfaces, state-to-state reaction dynamics, state-to-state tetra-atomic reaction dynamics using transition wave packet method and reactant coordinate method, and electronic dynamics in H 2 + and H 2 molecules will be presented.

show abstract

Section: Multidomain Spectral Element Methodsmentioning

confidence: 99%

Electronic and Molecular Dynamics by the Quantum Wave Packet Method

Sun

2016

Research Advances in Quantum Dynamics

Self Cite

View full text Add to dashboard Cite

show abstract

“…[15] To solve this problem, Patchkovskii et al have proposed a parallel method, [18] and achieved the spa-tial derivatives of the radial coordinate by using the finitedifference method (FDM), which leads to an increase in the grids for the larger sized problem, [17] and finally significantly increasing the amount of computation in the case of higher accuracy. [19] Guan et al solved TDSE of two-electron quantum system in spherical coordinates efficiently based on the finite-element (FE) discrete-variable-representation (DVR) and Short-Iteration-Lanczos (SIL) propagator, [20] because the FE-DVR can offer higher computing accuracy [21] and make the Hamiltonian matrix very sparse, whose effects are similar to those provided by the B-spline [22,23] and sine-DVR, [24] and the efficiency of the wave function evolution strongly relies on the sparsity of the Hamiltonian matrix for the SIL propagator. [25] The most ideal structure of the Hamiltonian matrix is expected to have diagonal or similarly sparse elements for the SIL propagator.…”

Section: Introductionmentioning

confidence: 99%

Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field*

Zhou¹,

Liu²,

Liu³

et al. 2019

Chinese Phys. B

View full text Add to dashboard Cite

We present a parallel numerical method of simulating the interaction of atoms with a strong laser field by solving the time-depending Schrödinger equation (TDSE) in spherical coordinates. This method is realized by combining constructing block diagonal matrices through using the real space product formula (RSPF) with splitting out diagonal sub-matrices for short iterative Lanczos (SIL) propagator. The numerical implementation of the solver guarantees efficient parallel computing for the simulation of real physical problems such as high harmonic generation (HHG) in these interaction systems.

show abstract

Dimension of discrete variable representation for mixed quantum/classical computation of three lowest vibrational states of OH stretching in liquid water

Jeon

Yang

2017

The Journal of Chemical Physics

View full text Add to dashboard Cite

Three low-lying vibrational states of molecular systems are responsible for the signals of linear and third-order nonlinear vibrational spectroscopies. Theoretical studies based on mixed quantum/classical calculations provide a powerful way to analyze those experiments. A statistically meaningful result can be obtained from the calculations by solving the vibrational Schrödinger equation over many numbers of molecular configurations. The discrete variable representation (DVR) method is a useful technique to calculate vibrational eigenstates subject to an arbitrary anharmonic potential surface. Considering the large number of molecular configurations over which the DVR calculations are repeated, the calculations are desired to be optimized in balance between the cost and accuracy. We determine a dimension of the DVR method which appears to be optimum for the calculations of the three states of molecular vibrations with anharmonic strengths often found in realistic molecular systems. We apply the numerical technique to calculate the local OH stretching frequencies of liquid water, which are well known to be widely distributed due to the inhomogeneity in molecular configuration, and found that the frequencies of the 0-1 and 1-2 transitions are highly correlated. An empirical relation between the two frequencies is suggested and compared with the experimental data of nonlinear IR spectroscopies.

show abstract

An improved Lobatto discrete variable representation by a phase optimisation and variable mapping method

Cited by 6 publications

References 70 publications

Electronic and Molecular Dynamics by the Quantum Wave Packet Method

Electronic and Molecular Dynamics by the Quantum Wave Packet Method

Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field*

Dimension of discrete variable representation for mixed quantum/classical computation of three lowest vibrational states of OH stretching in liquid water

Contact Info

Product

Resources

About