Proton tunneling in low dimensional cesium silicate LDS-1

In low dimensional cesium silicate LDS-1 (monoclinic phase of CsHSi₂O₅), anomalous infrared absorption bands observed at 93, 155, 1210, and 1220 cm^-1 are assigned to the vibrational mode of protons, which contribute to the strong hydrogen bonding between terminal oxygen atoms of silicate chain (O-O distance = 2.45 Å). The integrated absorbance (oscillator strength) for those modes is drastically enhanced at low temperatures. The analysis of integrated absorbance employing two different anharmonic double-minimum potentials makes clear that proton tunneling through the potential barrier yields an energy splitting of the ground state. The absorption bands at 93 and 155 cm^-1, which correspond to the different vibrational modes of protons, are attributed to the optical transition between the splitting levels (excitation from the ground state (n = 0) to the first excited state (n = 1)). Moreover, the absorption bands at 1210 and 1220 cm^-1 are identified as the optical transition from the ground state (n = 0) to the third excited state (n = 3). Weak Coulomb interactions in between the adjacent protons generate two types of vibrational modes: symmetric mode (93 and 1210 cm^-1) and asymmetric mode (155 and 1220 cm^-1). The broad absorption at 100-600 cm^-1 reveals an emergence of collective mode due to the vibration of silicate chain coupled not only with the local oscillation of Cs⁺ but also with the proton oscillation relevant to the second excited state (n = 2).