Related Experiment Video
Updated: May 2, 2026
10:52
Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
Published on: April 12, 2019
14.1K
Improving the efficiency of Monte Carlo surface hopping calculations
1Department of Chemistry, Tulane University , New Orleans, Louisiana 70118, United States.
The Journal of Physical Chemistry. B
|March 22, 2014
Summary
This study enhances surface hopping semiclassical calculations using Monte Carlo methods. Averaging trajectory sections and employing Sobol sequences improve numerical efficiency and accuracy with fewer samples.
Area of Science:
- Quantum chemistry
- Computational physics
- Chemical dynamics
Background:
- Semiclassical methods are crucial for simulating quantum dynamics.
- Surface hopping is a common technique to model non-adiabatic transitions.
- Improving the efficiency and accuracy of these methods is an ongoing challenge.
Purpose of the Study:
- To investigate a Monte Carlo-based surface hopping method for semiclassical calculations.
- To enhance the numerical efficiency of the surface hopping approach.
- To assess the impact of trajectory sampling techniques on accuracy.
Main Methods:
- A surface hopping method incorporating a Monte Carlo procedure for hop decisions.
- Averaging over multiple copies of trajectory sections within interaction regions.
- Utilizing Sobol sequences for selecting initial trajectory momentum.
Main Results:
- Numerical efficiency is improved by averaging trajectory sections.
- Accurate results are achievable with reduced trajectory sample sizes.
- Sobol sequences demonstrate effectiveness in trajectory initializations.
Conclusions:
- The proposed Monte Carlo surface hopping method offers improved efficiency.
- Averaging trajectory segments and using Sobol sequences are effective strategies.
- This approach enables accurate semiclassical calculations with smaller computational cost.
Related Concept Videos
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
438
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
438
01:20Maxwell-Boltzmann Distribution: Problem Solving
2.3K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
2.3K
01:16Energy Conservation and Bernoulli's Equation
7.2K
Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
7.2K
01:24Numerical Calculations
1.3K
In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...
1.3K
01:29Reaction Mechanisms: Rate-limiting Step Approximation
100
The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
100
01:28Methods of Medium Optimization
70
Optimizing growth media enhances microbial proliferation and maximizes product yield. Statistical experimental design methodologies provide structured and reproducible approaches, offering progressively higher levels of robustness and efficiency.The One-Factor-at-a-Time (OFAT) MethodThe One-Factor-at-a-Time (OFAT) method involves adjusting a single variable while keeping all others constant. However, it cannot detect interactions between variables, often leading to suboptimal outcomes when...
70