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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Significant Figures in Calculations

Significant Figures in Calculations

Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be determined by the following rules for rounding numbers:

Quantitative Aspects of Drug-Receptor Interaction

Quantitative Aspects of Drug-Receptor Interaction

The receptor occupancy theory connects a drug's response to the number of occupied receptors. With higher drug concentrations, more receptors are occupied, leading to increased responses. The formation of drug-receptor complexes involves association and dissociation rates, which reach equilibrium when the forward and backward reactions are equal. The equilibrium association constant (Ka) and its inverse, the equilibrium dissociation constant (Kd), indicate drug affinity. Higher Ka and lower...

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Updated: Mar 6, 2026

Experimental Quantification of Interactions Between Drug Delivery Systems and Cells In Vitro: A Guide for Preclinical Nanomedicine Evaluation

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Uncertainty Quantification for In Silico Chemistry.

Tom Frömbgen¹, Elizaveta Surzhikova², Jürgen Dölz³

¹Mulliken Center for Theoretical Chemistry, Clausius-Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstraße 4, 53115 Bonn, Germany.

Chemical Reviews

|March 4, 2026

Summary

This summary is machine-generated.

Uncertainty quantification (UQ) is becoming crucial for in silico chemistry. This review establishes a common language and surveys UQ methods to improve the reliability of computational chemistry predictions.

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Area of Science:

Computational Chemistry
Data Science

Background:

Worldwide computing power has advanced in silico chemistry, enabling property and process predictions.
Abundant data from quantum chemistry, molecular dynamics, and machine learning necessitate robust error and uncertainty assessment.
Uncertainty quantification (UQ) provides mathematical frameworks to address accuracy, precision, and reliability in computational chemistry.

Purpose of the Study:

To establish a common language for UQ in the context of in silico chemistry.
To introduce key mathematical formalisms for UQ.
To survey the application of UQ across various in silico chemistry domains.

Main Methods:

Literature review of uncertainty quantification in computational chemistry.
Explanation of mathematical frameworks relevant to UQ.
Categorization of UQ applications in different areas of in silico chemistry.

Main Results:

A unified perspective on UQ for in silico chemistry is presented.
Key mathematical approaches for quantifying uncertainty are detailed.
A comprehensive overview of current UQ applications in computational chemistry is provided.

Conclusions:

UQ is essential for enhancing the trustworthiness of in silico chemistry predictions.
Standardized language and methods for UQ will accelerate its adoption.
The integration of UQ offers deeper insights into chemical phenomena and improves decision-making in research.