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Compared with conventional, physical measurements, the cost of computational modeling continues to drop. This has driven many industries to incorporate computational predictions in their R&D processes. However, to replace a physical measurement, the quantitative reliability of a computational prediction must be known. That is, its associated uncertainty must be known. The goal of this project is to change current practice, so that ISO-style virtual measurements, which we are defining as a value with an uncertainty, supplant "computed values." The scope of this project is to provide uncertainties for common predictions from computational quantum chemistry.


Figure with data points and lines, with the x axis labeled “unreliability” and the y axis labeled “error”.

Figure showing the relationship between error and reliability for predicted properties. 

Credit: NIST

Intended Impact

When engineering data, such as for reactive-chemical hazards, are obtained using quantum chemistry, the lack of associated uncertainties means that the reliability of the data is poorly known. Safety thus requires a skeptical view, often leading to expensive over-design.


Predictions from quantum chemistry will carry meaningful uncertainties, allowing such predictions to be used as drop-in replacements for expensive, time-consuming, experimental measurements, in some applications. The dollar value of computational predictions will be greatly enhanced.


In the near- and intermediate-term, the most success is anticipated for predictions related to thermochemistry and vibrational spectroscopy, which are interrelated via statistical mechanics. These applications are relevant for chemical engineering, analytical chemistry, and academic physical chemistry. They are also two of the three most common applications of quantum chemistry. The third common application, molecular structure is a lower-priority goal.

Research Activities and Technical Approach

The flagship project in this research program is the popular Computational Chemistry Comparison and Benchmark Database (NIST Standard Reference Database 101; This website includes evaluated experimental data for more than 1400 selected chemical compounds, plus more than 400,000 property predictions using a variety of methods from quantum chemistry. Integrated software tools allow users to answer the benchmarking questions that are required by current, accepted best practice. However, the CCCBDB does not generally make recommendations. That is the role of the other project in this program, which relies heavily upon the CCCBDB. This collaboration with ITL makes recommendations for obtaining and using uncertainties. All recommendations follow the ISO Guide to the Expression of Uncertainty in Measurement. Recommendations include vibrational spectroscopy, vibrational zero-point energies (ZPEs), and vibrational spectroscopy from second-order vibrational perturbation theory (VPT2).

Major Accomplishments

  • CCCBDB Version 16 in early 2013.
  • Evaluated reference data for experimental ZPEs.
  • Scaling factors/uncertainties for ZPEs.
  • Scaling factors/uncertainties for VPT2 theory.

Associated Product(s)

NIST Standard Reference Database 101: Computational Chemistry Comparison and Benchmark Database (

It is expanded to include 1400 molecules and more than 400,000 computational predictions, including new properties and molecule types.


  1. Irikura, K.K., New Empirical Procedures for Improving ab Initio Energetics, J. Phys. Chem. A, 106, 9910-9917 (2002).
  2. Irikura, K.K., Johnson, R.D., III, Kacker, R.N., Uncertainty Associated with Virtual Measurements from Computational Quantum Chemistry Models, Metrologia, 41, 369-375 (2004).
  3. Irikura, K.K., Johnson, R.D., III, Kacker, R.N., Uncertainties in Scaling Factors for ab Initio Vibrational Frequencies, J. Phys. Chem. A, 109, 8430-8437 (2005).
  4. Irikura, K.K., Experimental Vibrational Zero-Point Energies: Diatomic Molecules, J. Phys. Chem. Ref. Data, 36, 389-397 (2007).
  5. Irikura, K.K., Johnson, R.D., III, Kacker, R.N., Kessel, R., Scaling Factors and Uncertainties for ab Initio Anharmonic Vibrational Frequencies, J. Chem. Theory Comput., 2010, 6 (9), pp 2822-2828
  6. Jacobsen, R., Johnson, R.D., III, Irikura, K.K., Kacker, R.N, Anharmonic Calculations are Not Worthwhile for Small Basis Sets, J. Chem. Theory Comput., 2013, 9 (2), pp 951–954
Created February 13, 2009, Updated November 7, 2023