Molecular Quantum Dynamics by Fabien Gatti

Author:Fabien Gatti
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

Fig. 5.3Computed IR spectra of the (a) H(H2O)2 +, (b) D(D2O)2 +, (c) H(D2O)2 +, and (d) D(H2O)2 + isotopologues of the Zundel cation with assignments of the most important peaks

Figure 5.3 presents the IR spectra of H(H2O)2 +, D(D2O)2 +, H(D2O)2 + and D(H2O)2 +. The lowest frequency parts of the four spectra are composed of two lines related to the one-quantum wagging motions and its combination with the internal rotation motion of one of the monomers with respect to the other. The highest frequency parts of the spectra are composed of two bright lines related to the terminal O–H(D) vibrations of the water molecules. Neither the assignment of the just discussed peaks in the lowest and highest energy domain nor the relative positions between each other change after deuteration. Only the expected red-shifts take place for D(D2O)2 + and H(D2O)2 +, i.e. when the terminal hydrogens are substituted by deuterium atoms.

The situation turns out to be much more complex in the spectral region between 600 and 2,000 cm−1. The middle range spectrum of the H(H2O)2 + cation in Fig. 5.3a features five clearly visible absorptions in the range between 900 and 1,900 cm−1. They could be assigned and explained as arising from a set of five coupled zeroth-order states composed of [8, 10]: , a combination of two modes, a two-quanta asymmetric wagging (w 3) mode and the one-quantum (1R) mode, where R is the O–O stretching coordinate; | Φ 1z ⟩, the one-quantum asymmetric proton stretch along the central O–O axis (z refers to the proton position along the O–O axis); | Φ 1z, 1R ⟩, the combination of the 1z and 1R excitations; | Φ 1z, 2R ⟩, the combination of the 1z and two-quanta O–O excitations; | Φ bu ⟩, the ungerade water-bending mode.

The most intense line of the H(H2O)2 + spectrum centered at 1,040 cm−1 is related to the (1z) transition since the displacement of the central proton along the O–O axis causes the largest variation of the dipole moment. Thus the | Φ 1z ⟩ zeroth-order state has a large contribution to this eigenstate, but the second most important contribution to this line arises from the zeroth-order state. The situation is reversed for the transition centered at 915 cm−1, whose leading contribution is and the second most important one is | Φ 1z ⟩. Therefore the doublet of peaks centered at about 1,000 cm−1 in the H(H2O)2 + arises from a Fermi resonance between the strongly coupled, zeroth-order states | Φ 1z ⟩ and [8, 10, 11]. The next three lines of the spectrum correspond to the 1,415 cm−1 (1z, 1R), 1,750 cm−1 (bu) and 1,905 cm−1 (1z, 2R) transitions, respectively. All three transitions, and specially (bu), have a non-negligible contribution from the | Φ 1z ⟩ zeroth-order state, from which they obtain a large part of their spectral intensity [10]. Moreover, the strong coupling between the | Φ 1z ⟩ and | Φ bu ⟩ modes is responsible for shifting the (1z) and (bu) lines about 150 cm−1 down and up, respectively, with respect to their estimated uncoupled positions [10, 11].

The IR spectrum of D(D2O)2 + is shown in Fig. 5.3b. The (1z) peak is found here at 678 cm−1 and is, as in H(H2O)2 +, the most intense IR absorption.

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