A QUANTUM-CLASSICAL APPROACH TO MOLECULAR DYNAMICS

2003 ◽  
Vol 02 (01) ◽  
pp. 73-90 ◽  
Author(s):  
G. D. BILLING
Keyword(s):  
Wave Function ◽  
Classical Mechanics ◽  
Basis Set ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Molecular Systems ◽  
Order Expansion ◽  
Classical Trajectories ◽  
Grid Points ◽  
Variable Representation

We present a new method for treating the dynamics of molecular systems. The method has been named "quantum dressed" classical mechanics and is based on an expansion of the wave function in a time-dependent basis-set, the Gauss–Hermite basis-set. From here it is possible to proceed in two ways, one is in principle exact and the other approximate. In the exact approach one constructs a discrete variable representation (DVR) in which the grid points are defined by the Hermite part of the Gauss–Hermite basis set. In the approximate method a second order expansion of the potential around the classical trajectories is introduced and the quantum dymamics solved in a second quantization rather than a wave-function representation.

Discrete variable representation of the Smoluchowski equation using a sinc basis set

2015 ◽  
Vol 17 (26) ◽  
pp. 17362-17374 ◽  
Author(s):  
Andrea Piserchia ◽  
Vincenzo Barone
Keyword(s):  
Smoluchowski Equation ◽  
Basis Set ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Variable Representation

We present a new general approach for the solution of the monodimensional Smoluchowski equation using a discrete variable representation (DVR).

NEARLY LINEAR SCALABILITY OF TIME-DEPENDENT DISCRETE VARIABLE REPRESENTATION (TDDVR) METHOD FOR THE DYNAMICS OF MULTI-SURFACE MULTI-MODE HAMILTONIAN

2013 ◽  
Vol 12 (05) ◽  
pp. 1350042 ◽  
Author(s):  
BASIR AHAMED KHAN ◽  
SUBHANKAR SARDAR ◽  
TAPAS SAHOO ◽  
PRANAB SARKAR ◽  
SATRAJIT ADHIKARI
Keyword(s):  
Quantum Dynamics ◽  
Radiative Decay ◽  
Electronic States ◽  
Photoelectron Spectra ◽  
Time Dependent ◽  
Basis Set ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Variable Representation ◽  
Multi Mode

Time-Dependent Discrete Variable Representation (TDDVR) method was implemented by involving "classical" trajectories on each degrees of freedom (DOF) for the dynamics of multi-surface multi-mode Hamiltonian. The major focus of this article is to explore the efficiency of the serial and parallelized TDDVR algorithm for relatively large dimensional quantum dynamics in presence of non-adiabaticity among the electronic states. As a model system, the complex photoelectron spectra and non-radiative decay dynamics of trifluoroacetonitrile radical cation ( CF3CN+ ) are theoretically simulated with the aid of such parallelized algorithm, where the five lowest electronic states (X2E, A2A1, B2A2, C2A1, and D2E) of the Hamiltonian are interconnected through several conical intersections in the vicinity of Frank–Condon region with twelve (12) active vibrational modes. The Jahn–Teller splitting of the X2E and D2E states makes the coupled five-surface system to a more challenging quantum dynamical seven-surface twelve-mode model. The results obtained from the TDDVR approach show very good agreement with the profiles of both Multi Configuration Time-Dependent Hartree (MCTDH) methodology and experimental technique, where its' sequencial and parallelized algorithm depict closely linear scalability with the increasing number of basis set vis-a-vis DOFs.

Rovibrational spectroscopic constants of the interaction between ammonia and metallo-phthalocyanines: a theoretical protocol for ammonia sensor design

2017 ◽  
Vol 19 (17) ◽  
pp. 10843-10853 ◽  
Author(s):  
Alan R. Baggio ◽  
Daniel F. S. Machado ◽  
Valter H. Carvalho-Silva ◽  
Leonardo G. Paterno ◽  
Heibbe Cristhian B. de Oliveira
Keyword(s):  
Dft Calculations ◽  
Theoretical Approach ◽  
Schrodinger Equation ◽  
Spectroscopic Constants ◽  
Sensor Design ◽  
Discrete Variable ◽  
Ammonia Sensor ◽  
Discrete Variable Representation ◽  
Representation Method ◽  
Variable Representation

We developed an adapted theoretical approach based on DFT calculations (B3LYP) and the nuclear Schrödinger equation using the Discrete Variable Representation method to model the interaction of ammonia with metallo-phthalocyanines.

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

2021 ◽  
Vol 323 ◽  
pp. 14-20
Author(s):  
Naranchimeg Dagviikhorol ◽  
Munkhsaikhan Gonchigsuren ◽  
Lochin Khenmedekh ◽  
Namsrai Tsogbadrakh ◽  
Ochir Sukh
Keyword(s):  
Excited States ◽  
Density Functional ◽  
Time Dependent ◽  
Discrete Variable ◽  
Coulomb Wave Function ◽  
Discrete Variable Representation ◽  
Density Functional Calculation ◽  
Imaginary Time ◽  
Sham Equation ◽  
Variable Representation

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.

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