A method is proposed for carrying out molecular dynamics simulations of processes that involve electronic transitions. The time dependent electronic Schrodinger equation is solved self‐consistently with the classical mechanical equations of motion of the atoms. At each integration time step a decision is made whether to switch electronic states, according to probabilistic ‘‘fewest switches’’ algorithm. If a switch occurs, the component of velocity in the direction of the nonadiabatic coupling vector is adjusted to conserve energy. The procedure allows electronic transitions to occur anywhere among any number of coupled states, governed by the quantum mechanical probabilities. The method is tested against accurate quantal calculations for three one‐dimensional, two‐state models, two of which have been specifically designed to challenge any such mixed classical–quantal dynamical theory. Although there are some discrepancies, initial indications are encouraging. The model should be applicable to a wide variety of gas‐phase and condensed‐phase phenomena occurring even down to thermal energies.

/pdf/molecular-dynamics-with-electronic-transitions-39jwikyow5.pdf

Molecular dynamics with electronic transitions

https://www.pci.uni-heidelberg.de/tc/usr/mctdh/lit/rev.pdf

The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets

A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies. The modified equations are also related to the perfectly matched layer that was presented recently for 2D wave propagation. Absorbing-material boundary conditions are of particular interest for finite-difference time-domain (FDTD) computations on a single-instruction multiple-data (SIMD) massively parallel supercomputer. A 3D FDTD algorithm has been developed on a connection machine CM-5 based on the modified Maxwell's equations and simulation results are presented to validate the approach. © 1994 John Wiley & Sons, Inc.

A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates

A new propagation scheme for the time dependent Schrodinger equation is based on a Chebychev polynomial expansion of the evolution operator U=exp(−iHt). Combined with the Fourier method for calculating the Hamiltonian operation the scheme is not only extremely accurate but is up to six times more efficient than the presently used second order differencing propagation scheme.

An accurate and efficient scheme for propagating the time dependent Schrödinger equation

https://www.physik.uni-augsburg.de/theo1/hanggi/Papers/213.pdf

Driven quantum tunneling

A fourier method solution for the time dependent Schrödinger equation as a tool in molecular dynamics

Absorbing boundaries for wave propagation problems

SUMMARY A new approach for viscoacoustic wave propagation is developed. The Boltzmann’s superposition principle based on the general standard linear solid rheology is implemented in the equation of motion by the introduction of memory variables. This approach replaces the conventional convolutional rheological relation, and thus the complete time history of the material is no longer required, and the equations of motion become a coupled first-order linear system in time. The propagation in time is done by a direct expansion of the evolution operator by a Chebycheff polynomial series. The resulting method is highly accurate and effects such as the numerical dispersion often encountered in time-stepping methods are avoided. The numerical algorithm is tested in the problem of wave propagation in a homogeneous viscoacoustic medium. For this purpose the l-D and 2-D viscoacoustic analytical solutions were derived using the correspondence principle.

/pdf/wave-propagation-simulation-in-a-linear-viscoacoustic-medium-4c5jcfq517.pdf

Wave propagation simulation in a linear viscoacoustic medium

https://ntrs.nasa.gov/api/citations/19900005532/downloads/19900005532.pdf

A modified Chebyshev pseudospectral method with an O(N –1 ) time step restriction

A new quantum mechanical time dependent integrator was used in the study of wave packet dynamics on potentials which include a deep well. The purpose of the study was to find the conditions, if any, for complex formation. The integrator, which is stable, conserves energy and norm and was used on the H++H2 system whose classical trajectory had been previously worked out. Almost no complex formation is found for the H++H2 system and its isotopic analogs. For high translational energies there was a good correspondence with the classical trajectory results, while for low translational energies where the classical trajectories become complex, the quantum calculations still show nonstatistical behavior. For even lower energies, a quantum effect took place leading to zero reactivity.

Dan Kosloff

Papers

A fourier method solution for the time dependent Schrödinger equation as a tool in molecular dynamics

Absorbing boundaries for wave propagation problems

Wave propagation simulation in a linear viscoacoustic medium

A modified Chebyshev pseudospectral method with an O(N –1 ) time step restriction

A Fourier method solution for the time dependent Schrödinger equation: A study of the reaction H++H2, D++HD, and D++H2