QVibeplot: A Program To Visualize Molecular Vibrations in Two

Jun 17, 2013 - Two-dimensionality is achieved by basing the representation on a skeletal formula of the molecule. The program also displays the spectr...
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QVibeplot: A Program To Visualize Molecular Vibrations in Two Dimensions Mathias Laurin* Lehrstuhl für Physikalische Chemie II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Egerlandstraße 3, 91058 Erlangen, Germany ABSTRACT: QVibeplot is a software program that automatically generates twodimensional visualizations of molecular vibrations. The representations show the changes of bond lengths, angles, and torsions occurring upon a vibration. This is consistent with the experimentalist’s understanding of molecular vibrations that makes a distinction between stretching and deformation modes. Twodimensionality is achieved by basing the representation on a skeletal formula of the molecule. The program also displays the spectrum and the list of frequencies. The phase and amplitude are indicated as well, providing a comprehensive visualization of molecular vibrations. The software is available online as a free and open-source software.

KEYWORDS: Upper-Division Undergraduate, Graduate Education/Research, Physical Chemistry, Inorganic Chemistry, Computer-Based Learning, Qualitative Analysis, Group Theory/Symmetry, IR Spectroscopy Topics, Raman Spectroscopy, Spectroscopy

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INTRODUCTION Vibrational spectroscopies of molecules are techniques used extensively in the fields of organic,1,2 inorganic,3 and analytical chemistry,4 life science,5−7 and physical chemistry.8,9 Infrared and Raman spectroscopies are therefore commonly taught from an experimental and a theoretical standpoint. Whereas calculated normal modes should provide a particularly elegant teaching aid, they are often difficult to interpret in experimental terms and thus barely used. The help of computational techniques is nevertheless important for the analysis of larger molecules. There exist a number of numerical approaches to vibrational frequency and normal coordinate calculation10,11 and these methods have been reviewed by Scott and Radom,12 and Head.13 The results of these computations are usually interpreted by visualizing the molecular vibrations. In the first part of this report, we critically review the three most common representations of vibrational analyses. We demonstrate that their major drawback lies in the fact that the vibrations are most often presented as atomic displacements instead of changes in the bonds. In the second part, we introduce a program presenting theoretical calculations in terms of changes of internal coordinates (stretching and deformations) that are familiar to the experimentalists. The illustrations generated thus help students to understand the relationships between the theoretical treatment of vibrations, the molecular movements, and the spectrum and its interpretation. © 2013 American Chemical Society and Division of Chemical Education, Inc.

COMMON REPRESENTATIONS OF VIBRATIONAL ANALYSES

Animation

A common presentation consists in showing animations of the molecule generated by programs such as Molden14 or Jmol.15 This method has the advantage of being particularly graphic and succeeds in creating the illusion of actual atomic vibrations. As such, it is suitable in front of a live audience. However, such representations are intrinsically three-dimensional so that the perception of the results depends on the projection plane. In addition, a vibrating molecule is shown as well for the nongenuine vibrations: translations and rotations, which is confusing. Tabulated Interpretation

Another method is the description of the vibrations in a table (see, e.g., p 264 in ref16). Such tables typically contain calculated frequencies, often compared with experimental values, and textual descriptions of the normal modes (symmetry, phase, and amplitude for example). This method, however, does not provide any visualization and the comparison of such tabulated data and experimental spectra is particularly laborious. Published: June 17, 2013 944

dx.doi.org/10.1021/ed300554z | J. Chem. Educ. 2013, 90, 944−946

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Technology Report

Vectorial Representation

Bézier curves. The amplitude of a bond-length change is given by the width of the marker. The radius of the arcs for angle changes is proportional to the amplitude of the change. The Bézier curves are drawn such that the middle of the curve is the closest (and may cross) the bond subjected to the torsion. The ends of the Bézier curve point toward the atoms in the planes subjected to the dihedral angle change. The length of the curve indicates the amplitude. The color always indicates the phase: the changes have the same sign if marked with the same color, or opposite signs if the colors are different. The advantages of the representation can be demonstrated within a brief, qualitative analysis of Figure 1. First, the visualization makes it evident that the stretching modes (last five, or Ag−B2u) appear at higher wavenumbers than deformations and that the double bond vibrates at a lower frequency. Also, on this planar molecule, bond torsions generate out-of-plane movements of the hydrogens, which are identified by the yellow and green curves (B2g, B3u, and Au). A more thorough inspection further reveals that in-phase and outof-phase vibrations appear next to each other. A detailed analysis is out of the scope of this report. One might as well concentrate on the markers and remark that the symmetry of the markers is the symmetry of the mode. Such a representation can therefore be useful in a group theory class as well. It is most easily illustrated by searching for “g” or “u” symmetries: for “u”, the markers for angle or bond-length changes have a different color upon inversion, and conversely for “g”, the color is conserved.

In vectorial representations, a projection of the molecule at equilibrium is displayed, and the displacements are represented as vectors starting at each atom (see, e.g., pp 29−31 or 100 in ref 16). It is a direct presentation of the vibrational analysis. But as with animations, the result strongly depends on the projection plane. Another point is that this method does not show the information chemists expect; molecular vibrations are not interpreted in terms of concerted atomic displacements but as stretching and deformations of chemical bonds.1,12,16 Such plots are therefore particularly difficult to interpret.

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QVIBEPLOT SOFTWARE FOR VIBRATIONAL ANALYSES

Overview

QVibeplot addresses the main limitations identified above. First, the vibrational analysis is displayed on a skeletal formula, a highly standardized two-dimensional representation of a molecule. Second, the changes due to the vibrations are displayed as changes of the bond geometry, which is the quantity relevant to vibrational spectroscopy. Ethene Example

Sobota et al. published examples of usage of QVibeplot on larger nonplanar molecules. 17,18 We chose instead to demonstrate the program with a simple example. The complete analysis of the normal modes of ethene (C2H4) is shown in Figure 1. Selecting the frequencies in order produces such an

Installation

QVibeplot is available online under an open-source license. The program is written in Python19 with a PyQt420 graphical user interface. The input files are parsed using Pybel21 and the Open Babel22 libraries. The graphs are generated with the help of the Matplotlib library,23 which is used extensively. After downloading the program from http://vibeplot.sf.net, it may be installed on Windows by double-clicking on the executable file or extracting the archive to an empty directory and starting the program called “QVibeplot”.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG) within the Excellence Cluster “Engineering of Advanced Materials” in the framework of the excellence initiative. Ioannis Nikiforidis, Institut für Physikalische und Theoretische Chemie, Friedrich-Alexander-Universität Erlangen-Nürnberg has kindly provided the calculation of the ethene molecule used to illustrate this article.

Figure 1. The vibrations of ethene C2H4 displayed using QVibeplot 0.13.1. The normal modes are labeled with their frequency in wavenumbers (cm−1) and their symmetry. The colored markings are explained in the text.

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overview of calculated vibrations. The molecule contains six atoms, and therefore, there are 3 × 6 − 6 = 12 normal modes.16 The normal modes are labeled with their frequency in wavenumbers (cm−1) and their symmetry and are ordered from the lowest wavenumbers to the highest. Changes of bond length (i.e., stretching) are indicated by coloring the bond; changes of bond angle, with colored arcs; and torsions, with

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