Description of Aromaticity with the Help of Vibrational ... in view of the properties of the...

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  • Description of Aromaticity with the Help of VibrationalSpectroscopy: Anthracene and PhenanthreneRobert Kalescky, Elfi Kraka, and Dieter Cremer*

    Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University,3215 Daniel Avenue, Dallas, Texas 75275-0314, United States

    *S Supporting Information

    ABSTRACT: A new approach is presented to determine -delocalizationand the degree of aromaticity utilizing measured vibrational frequencies.For this purpose, a perturbation approach is used to derive vibrationalforce constants from experimental frequencies and calculated normalmode vectors. The latter are used to determine the local counterparts ofthe vibrational modes. Next, relative bond strength orders (RBSO) areobtained from the local stretching force constants, which provide reliabledescriptors of CC and CH bond strengths. Finally, the RBSO values for CC bonds are used to establish a modified harmonic oscillatormodel and an aromatic delocalization index AI, which is split into a bond weakening (strengthening) and bond alternation part. In thisway, benzene, naphthalene, anthracene, and phenanthrene are described with the help of vibrational spectroscopy as aromatic systemswith a slight tendency of peripheral -delocalization. The 6.8 kcal/mol larger stability of phenanthrene relative to anthracenepredominantly (84%) results from its higher resonance energy, which is a direct consequence of the topology of ring annelation.Previous attempts to explain the higher stability of phenanthrene via a maximum electron density path between the bay H atoms aremisleading in view of the properties of the electron density distribution in the bay region.

    INTRODUCTIONThe description of the chemical bond is one of the majorobjectives in chemistry. The large variety of atomatominteractions, which reaches from strong covalent to weakelectrostatic interactions has been investigated with bothexperimental and quantum chemical, i.e., computational tools.13

    Special focus has been on the description of bonding in cyclicconjugated systems, which obtain via -electron delocalizationspecial properties. The conceptual approach to the description ofthese systems is summarized under the terms aromaticity andantiaromaticity.49

    There are numerous experimental and computationalinvestigations of aromatic or antiaromatic -electron systems.A quantification of the (anti)aromatic character of a moleculewith the help of its stability (energy), structure (geometry),reactivity, or spectroscopic properties fills myriads of primary andsecondary articles, only some of which can be mentionedhere.410 However, most investigations on aromaticity have beenbased on calculated rather than measured quantities. This has todo with limitations faced by experiments.Stability measurements of destabilized antiaromatic com-

    pounds are difficult and, apart from this, measured energies arenot accurate enough to detect some of the finer effects of electrondelocalization in distorted, strained, or charged cyclic -systems.Molecular parameters such as bond lengths provide a betteraccount of structural changes caused by (anti)aromaticity;however, X-ray, r0, ra, rz, etc. geometries are difficult to compareapart from the problem that bond lengths are not reliable bondstrength and -delocalization descriptors.11 Much work has beencarried out utilizing the magnetic properties;4,7,9 however, the

    NMR chemical shift of an atomic nucleus is also affected by morethan just -delocalization effects. Similarly, NMR spinspincoupling constants are inappropriate measures for a change in thebond strength as caused by -delocalization.12

    Up to this time, the vibrational properties of a molecule havehardly been used to describe the aromatic or antiaromaticcharacter of a conjugated cyclic molecule in a systematic way.13,14

    In view of the high accuracy, by which, e.g., vibrationalfrequencies can be measured, they should provide a sensitivemeasure for the degree of -delocalization and thereby alsoaromaticity in a molecule. Of course, one could argue that forantiaromatic and thereby destabilized molecules, the measure-ment of vibrational properties is as difficult as that of othermolecular properties. However, low temperature matrix isolationspectroscopy15 makes the measurement of vibrational spectra oflabile compounds possible. Also, reliable vibrational frequenciescan conveniently be calculated as second-order responseproperties and, when augmented by anharmonicity correc-tions,16,17 they are close to experimental frequencies.There is, however, the argument that vibrational frequencies

    are not suitable descriptors because they depend on atomicmasses and cannot be associated with special bonds because thevibrational normal modes are delocalized over the framework ofthe molecule as a result of modemode coupling.11,1820 In thiswork, we will show that both problems can be solved and thatmeasured experimental frequencies provide an excellent tool for

    Received: September 16, 2013Revised: November 30, 2013Published: December 5, 2013


    2013 American Chemical Society 223 | J. Phys. Chem. A 2014, 118, 223237

  • describing the aromatic character of a molecule. We willinvestigate benzene (1) and the benzoid polycyclic hydrocarbonsnaphthalene (2), anthracene (3), and phenanthrene (4) (seeFigure 1), for which all 3N 6 = Nvib (N: number of atoms)vibrational frequencies have been measured.2129 We willdemonstrate that by (i) using vibrational frequencies todetermine an experimentally based force constant matrix, (ii)using the force constants and auxiliary calculations to extractlocal vibrational modes, which can be assigned to individualbonds, and (iii) determining local stretching force constantsbased on the experimental frequencies, which are no longerflawed by mass effects or modemode coupling, we obtain asensitive measure for the strength of the chemical bonds in acyclic conjugated molecule as it results from -delocalization.A local stretching mode30,31 probes the strength of a bond by

    distorting it without changing its electronic structure. As a matterof fact, its stretching force constant and frequency relate to aninfinitesimal change of the bond. The force constant reflects thecurvature of the adiabatic BornOppenheimer potential energysurface (PES) in the direction of the internal coordinate with whichit is associated. As long as the BornOppenheimer approximation isappropriate, which is the case for all molecules investigated in thiswork, the local stretching force constants provide excellent bondstrength descriptors as was shown in previous work.3136

    Once a set of bond strength descriptors in the form ofstretching force constants has been derived from theexperimental frequencies, these can be converted for easier useinto relative bond strength orders (RBSO) choosing appropriatereference bonds. The RBSO values can be applied in connectionwith the Harmonic Oscillator Model of Aromaticity (HOMA)3740

    to determine the degree of aromaticity. Furthermore, we willinvestigate the question of whether the interactions between theCHbonds of the bay region of phenanthrene leads to any stabilizationand whether this is the cause for its increased stability compared tothat of anthracene.4145

    In this work, we will demonstrate that vibrational spectroscopycan provide reliable information about aromatic molecules. Theresults of this work will be presented in the following way. InSection 2, the computational methods and details will bedescribed. The normal and local vibrational frequencies of thetarget molecules will be discussed in Section 3, whereas inSection 4 RBSO and HOMA parameters for the analysis of thearomatic character of the target molecules will be presented.Finally, in Section 5, the conclusions of this work will besummarized.

    COMPUTATIONAL METHODSExperimental frequencies for benzene,21 naphthalene,22 anthra-cene,2328 and phenanthrene29 as well as the reference moleculesmethane,21 ethane,21 ethene,21 and acetylene21 were taken fromthe literature. The force constant matrix associated with acomplete set of 3N 6 vibrational frequencies can bedetermined utilizing the Wilson equation of vibrational spec-troscopy:18

    = F D G Dq 1 (1)

    where Fq is the calculated force constant matrix expressed ininternal coordinates qn,D collects the vibrational eigenvectors din form of column vectors ( = 1, , Nvib with Nvib = 3N L; N:number of atoms; L: number of translations and rotations), G isthe Wilson matrix for the kinetic energy,18 and is a diagonalmatrix containing the vibrational eigenvalues = 4

    2c22 . In the

    expression for the eigenvalues, represents the vibrationalfrequency of mode d. MatrixG can be determined with the helpof the atomic masses and the B matrix

    = G BM B1 (2)

    where B is a rectangular (Nvib 3N) matrix containing the firstderivatives of the internal coordinates with regard to the

    Figure 1.Target and reference molecules with numbering of atoms. For simplifying the discussion, specific CH and CC bonds are denoted as i (inner), c(central), b (bridge), or by Greek symbols.

    The Journal of Physical Chemistry A Article | J. Phys. Chem. A 2014, 118, 223237224

  • Cartesian coordinates. Hence, the force constant matrix Fq

    associated with the experimental frequencies can only bedetermined if, by an appropriate quantum chemical calculation,the normal mode vectors collected in the matrix D aredetermined. Clearly, the true mode matrix D will differ from