Multidimensional reactive scattering with quantum trajectories: Dynamics with Morse vibrational modes

Babyuk, Dmytro; Wyatt, Róbert E.

doi:10.1063/1.2218335

Cited by 20 publications

(13 citation statements)

References 33 publications

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“…Bohm's interest was primarily philosophical and interpretive -although the computational benefits of his approach have come to be greatly appreciated in recent years [13,[35][36][37][38], especially by members of the chemical quantum dynamics community [13,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. In Bohm's pilot wave theory, a system comprises both a wave and a particle [12].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the earliest calculations of quantum trajectories were always performed in a manner consistent with the logically causal relationships of Bohm's theory itself -i.e., Wðx; tÞ was computed first, only after which the quantum trajectory (or trajectory ensemble) was constructed from Wðx; tÞ. Such an approach, now called ''analytical," [13,37,36,38] stands in stark contrast to more recent ''synthetic" quantum trajectory methodologies (QTM's) [13,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53], in which both the trajectories and the wavefunction are computed numerically on-the-fly, each affecting the propagation of the other, like electric and magnetic fields in an EM wave.…”

Section: Introductionmentioning

confidence: 99%

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Bohmian mechanics without pilot waves

Poirier

2010

Chemical Physics

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bohmian mechanics without pilot waves

Poirier

2010

Chemical Physics

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“…Comparison of the reaction probabilities calculated by an exact method (solid lines) and by the quantum trajectory method (points) with initial kinetic energy E k equal to 0.0179 (1), 0.0280 (2), 0.0403 (3), and 0.0717(4).…”

mentioning

confidence: 99%

“…One such approach is the quantum trajectory method (QTM) [2,3]. This method has recently been used to calculate reaction probabilities for a model system consisting of 200 degrees of freedom [4]. Attempts to use QTM for actual systems have not yet been very successful due to singularities arising at nodes of the wave functions arising due to interferences of parts of the reflected and incident wave packet.…”

mentioning

confidence: 99%

“…The spatial derivatives are more difficult to determine since they must be calculated in an unstructured lattice. This is best performed by approximation using the method of least squares with a sliding weight as described in our previous work [8,9]. The tentative boundary between the reaction products and reagents was taken as the line traversing the origin through the saddle point on the PES.…”

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confidence: 99%

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Quantum trajectory method calculation of collinear collisions in the hydrogen exchange reaction H + ClH′ → HCl + H′

Babyuk

Nechiporuk

2009

Theor Exp Chem

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The quantum trajectory method was used to study the collinear reaction H + ClH¢ ® HCl + H¢. The potential energy surface was calculated on the QCISD(T)/6-311++G(3df,3pd) level. The reaction probabilities are in good accord with the results obtained by solving the Schroedinger equation using the finite difference method.Collision theory has been used for calculating the rate constant of a chemical reaction. An important step in this approach is calculation of the reaction probability by studying the dynamics of the colliding particles under different initial conditions. Such an investigation in the framework of classical mechanics makes the calculation relatively inexpensive relative to computer time and resources. However, in reactions of light atoms, the wave properties of these atoms cannot be neglected since tunneling may distort the rate constant by an order of magnitude at low temperatures. A rigorous quantum mechanical approach is possible only for reaction systems encompassing not more than five atoms since computer resources increase exponentially with increasing degrees of freedom. The present record is for the study of the reaction H 2 + C 2 H ® H + C 2 H 2 , in which there are nine degrees of freedom. A calculation for the probability for one initial state using a computer cluster consisting of 64 processors took 168 h [1]. Thus, there is an obvious need for alternative quantum methods permitting us to economize on computer resources. One such approach is the quantum trajectory method (QTM) [2,3]. This method has recently been used to calculate reaction probabilities for a model system consisting of 200 degrees of freedom [4]. Attempts to use QTM for actual systems have not yet been very successful due to singularities arising at nodes of the wave functions arising due to interferences of parts of the reflected and incident wave packet. For example, for the simplest system in the hydrogen exchange reaction H + H¢H ® H¢ + H 2 , strong interference makes the use of QTM impossible. On the other hand, we have already noted the possibility of using QTM for collinear light atom-heavy atom-light atom collisions. Thus, in the present work, we selected the reaction H + ClH¢ ® HCl + H¢ and the probability of this reaction was calculated using QTM.The initial step in collision theory is the Born-Oppenheimer principle and calculation of the potential energy surface. Electron correlation plays an important role in the system studied and many previous semiempirical methods have given different values of the potential barrier. Thus, the quantum-chemical calculations should be carried out on a high level. We selected QCISD/6-311++G(3df,3pd). The energy of the collinear ClH 2 system was calculated at 648 points using the GAUSSIAN03 package [5]. The potential energy surface (PES) obtained was virtually identical quantitatively with the PES calculated using a higher level ab initio method [6]. The height of the potential barrier on the calculated surface is 18.42 kcal/mol for r HCl = 2.79 Å. The surface has van der Waals...

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Two‐dimensional wavepacket dynamics with quantum hydrodynamics

Matsumoto

Hayashi

Ida

et al. 2007

Int J of Quantum Chemistry

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64112) which is based on quantum hydrodynamics to the quantum wavepacket dynamics and applied to several systems including tunneling and nonadiabatic transition. This approach is expected to overcome some disadvantages of the conventional wavepacket dynamics, such as order-N problem and use of absorbing potential. We applied this method to two-dimensional model of quantum tunneling system and compared the new approach with the conventional wavepacket simulation since the validity of this method to multidimensional systems is not well known. In the simulation, we adopted two different model potentials (Model I and Model II) and calculated time dependence of the probability density and the tunneling probability in both models, where we showed explicitly that the results of the quantum hydrodynamics are identical with those of the conventional method. Using the moving grid and the regridding algorithm in the quantum hydrodynamics, we can effectively avoid order-N problem and use of the absorbing potential. In addition to these computational advantages, the flux vector is easily obtained by the quantum hydrodynamics and these vectors field helps us to intuitively understand detailed tunneling dynamics.

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Multidimensional reactive scattering with quantum trajectories: Dynamics with Morse vibrational modes

Cited by 20 publications

References 33 publications

Bohmian mechanics without pilot waves

Bohmian mechanics without pilot waves

Quantum trajectory method calculation of collinear collisions in the hydrogen exchange reaction H + ClH′ → HCl + H′

Two‐dimensional wavepacket dynamics with quantum hydrodynamics

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