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Quantum-Chemistry-Centered Normal Coordinate Analysis (QCC-NCA): Application of NCA for the Simulation of the Vibrational Spectra of Large Molecules

  1. Nicolai Lehnert

Published Online: 15 SEP 2009

DOI: 10.1002/0470862106.ia605

Encyclopedia of Inorganic Chemistry

Encyclopedia of Inorganic Chemistry

How to Cite

Lehnert, N. 2009. Quantum-Chemistry-Centered Normal Coordinate Analysis (QCC-NCA): Application of NCA for the Simulation of the Vibrational Spectra of Large Molecules. Encyclopedia of Inorganic Chemistry. .

Author Information

  1. University of Michigan, Ann Arbor, MI, USA

Publication History

  1. Published Online: 15 SEP 2009


Vibrational spectroscopy is a powerful spectroscopic method that provides detailed information about the geometric and electronic structural properties of materials, compounds, and biomolecules. In the case of transition-metal complexes, for example, vibrational spectra allow for the determination of the oxidation and spin state of the metal. In addition, vibrational spectroscopy is of great value in monitoring the binding and activation of small molecules, especially diatomics X–Y (O2, N2, CO, NO, etc.) and their derivatives, by transition-metal complexes. Here, the coordination, reduction, protonation, derivatization, etc., of the diatomic can be monitored via the X–Y and metal-XY bond strengths. Usually, the corresponding X–Y and metal-XY vibrational frequencies are used for such correlations. This, however, is problematic because the energies of normal modes in general do not correlate directly with bond strengths, as they also depend on mode mixing and atomic masses. Because of this, it is much better to compare the X–Y and metal-XY force constants along a reaction coordinate or between different species to identify chemically important changes/differences in bond strengths. This poses one problem: force constants are obtained from normal coordinate analysis (NCA), but how can this type of analysis be performed routinely for large molecules with many vibrational degrees of freedom, especially if the interest is focused on a small subunit of the molecule (the metal-XY bond), whereas the other organic ligands L of the metal are of limited interest? The quantum chemistry centered normal coordinate analysis (QCC-NCA) provides a solution to this problem by using density functional theory (DFT) calculations to generate an initial force field, followed by refinement of the limited number of force constants of the metal-XY subunit only, whereas all other force constants remain unchanged. The available QCC-NCA software allows one to perform this kind of analysis with minimal effort. This article provides a general introduction to the QCC-NCA method and the underlying principles of vibrational analysis, combined with illustrative examples for applications from the area of the transition-metal mediated activation of N2, O2, and NO. Special focus is put on the electronic structures and reactivities of ferrous-heme nitrosyls, where the Fe–NO and N–O force constants have provided key insight into the activation of NO as a function of the trans ligand. The latest development with respect to the QCC-NCA method is the calculation of nuclear resonance vibrational spectroscopy (NRVS) intensities, which is described in the final sections of this article.


  • vibrational spectroscopy;
  • normal coordinate analysis;
  • force constants;
  • Raman spectroscopy;
  • nuclear resonance vibrational spectroscopy;
  • density functional theory calculations;
  • heme;
  • metalloporphyrins;
  • nitric oxide;
  • heme nitrosyls;
  • electronic structure