Related Experiment Video
Updated: Mar 29, 2026
12:11
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
8.8K
Determining the Numerical Stability of Quantum Chemistry Algorithms
Gerald Knizia1, Wenbin Li2, Sven Simon2
1Institut für Theoretische Chemie, Universität Stuttgart , Pfaffenwaldring 55, D-70569 Stuttgart, Germany.
Journal of Chemical Theory and Computation
|November 26, 2015
Summary
We developed a novel method to assess quantum chemistry algorithm stability by introducing controlled numerical noise. This technique reveals instabilities, like one in the Obara-Saika scheme, and guides precision choices for computations.
Area of Science:
- Computational Quantum Chemistry
- Numerical Analysis
- High-Performance Computing
Background:
- Accurate numerical properties of quantum chemistry algorithms are crucial for reliable computational results.
- Assessing numerical stability often requires significant programming effort or specialized tools.
- Floating-point precision limitations can impact the accuracy of complex quantum chemistry calculations.
Purpose of the Study:
- To introduce a broadly applicable and simple method for determining the numerical properties of quantum chemistry algorithms.
- To statistically analyze algorithm stability by introducing controlled numerical noise.
- To investigate the numerical stability of specific quantum chemistry schemes and assess the feasibility of using lower precision arithmetic.
Main Methods:
- A novel method involving automatic code injection of random numerical noise, comparable to floating-point precision, into computations.
- Statistical analysis of repeated algorithm runs with introduced noise to estimate numerical stability.
- Application of the method to evaluate the Obara-Saika integral scheme, coupled cluster perturbative triples, and density-fitted Møller-Plesset perturbation theory (MP2).
Main Results:
- A significant numerical instability was identified in a commonly used equation within the Obara-Saika integral evaluation scheme.
- Analysis suggests that coupled cluster perturbative triples can potentially be evaluated using single precision arithmetic.
- Insights were gained into optimizing the density fitting approximation for MP2 and identifying parts suitable for single precision.
Conclusions:
- The developed noise injection method provides a straightforward approach to assess numerical stability in quantum chemistry algorithms.
- The findings highlight potential numerical weaknesses in standard computational chemistry practices.
- Single precision arithmetic may be viable for certain calculations, particularly in orthogonal basis sets, provided long linear sums are avoided.
More Related Videos
Related Concept Videos
01:23Stability of Equilibrium Configuration
949
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
949
01:13Stability of Equilibrium Configuration: Problem Solving
1.2K
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Problem-solving in the context of the stability of equilibrium configuration...
1.2K
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
397
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...
397
02:30Stability of Substituted Cyclohexanes
17.3K
This lesson discusses the stability of substituted cyclohexanes with a focus on energies of various conformers and the effect of 1,3-diaxial interactions.
The two chair conformations of cyclohexanes undergo rapid interconversion at room temperature. Both forms have identical energies and stabilities, each comprising equal amounts of the equilibrium mixture. Replacing a hydrogen atom with a functional group makes the two conformations energetically non-equivalent.
For example, in...
The two chair conformations of cyclohexanes undergo rapid interconversion at room temperature. Both forms have identical energies and stabilities, each comprising equal amounts of the equilibrium mixture. Replacing a hydrogen atom with a functional group makes the two conformations energetically non-equivalent.
For example, in...
17.3K
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
01:59Relative Stabilities of Alkenes
16.1K
The relative stability of alkenes can be determined by comparing their heats of hydrogenation. The lower heat of hydrogenation indicates the more stable alkene. The three main factors determining the relative stability of alkenes are i) the number of substituents attached to the double-bond carbon atoms, ii) hyperconjugation, and iii) the stereochemistry of the double bond.
16.1K