Coupling frequency calculations, vibrational

But in a solid, the motions of the atoms are coupled together. The vibrational motion involves large numbers of atoms, and the frequency for these vibrations is less than the value used in equation (10.148). Thus, vibrations occur over a range of frequencies from v = 0 to a maximum u = vm. When this occurs the energy can be calculated by summing over all the frequencies. The... 

We have described our most recent efforts to calculate vibrational line shapes for liquid water and its isotopic variants under ambient conditions, as well as to calculate ultrafast observables capable of shedding light on spectral diffusion dynamics, and we have endeavored to interpret line shapes and spectral diffusion in terms of hydrogen bonding in the liquid. Our approach uses conventional classical effective two-body simulation potentials, coupled with more sophisticated quantum chemistry-based techniques for obtaining transition frequencies, transition dipoles and polarizabilities, and intramolecular and intermolecular couplings. In addition, we have used the recently developed time-averaging approximation to calculate Raman and IR line shapes for H20 (which involves... 

In any force-field model, the molecule to be analyzed is treated as a set of masses cormected by springs. Calculating vibrational frequencies for a particular set of coupled masses and springs is essentially a problem of matrix algebra, and the summary presented below is more mathematically intense than preceding sections. The equations may appear... 

A vibronic coupling model Hamiltonian was constructed using CASSCF (active space and basis set as discussed above for the semi-classical study) (79). The vibrational modes were obtained from a Hartree-Fock frequency calculation of the dianion, and it... 

Detailed measurements have been made of the low-frequency Raman spectra of [Zn(py)2X2] (X = C1 or Br) and of the far-IR spectra of the complex where X = Q at liquid nitrogen temperature. It is found that skeletal molecular vibrations couple with lattice vibrations in the crystal, except for the Zn—X stretching vibrations. Force constant calculations indicate the Zn—N bond to be stronger in the bromide, while the Zn—Cl bond is stronger than the Zn—Br bond.477... 

An impressive application of infrared and Raman spectroscopy was demonstrated in studies of superelectrophilic diprotonated thiourea, [H3NGSH jNfE 2+ 2AsFf,. The Raman spectrum (taken at — 110°C) corresponded reasonably well with calculated vibrational bands predicted by density functional theoiy.38 Coupled with computational methods for predicting vibrational frequencies, it is expected that vibrational spectroscopic techniques will be useful for the observations of these and other superelectrophiles. 

In the present paper, we show that it is possible to calculate both vibrational and electronic transitions of H2SO4 with an accuracy that is useful in atmospheric simulations. We calculate the absorption cross sections from the infrared to the vacuum UV region. In Section 2 we describe the vibrational local mode model used to calculate OH-stretching and SOH-bending vibrational transitions as well as their combinations and overtones [42-44]. This model provides frequencies and intensities of the dominant vibrational transitions from the infrared to the visible region. In Section 3 we present vertical excitation energies and oscillator strengths of the electronic transitions calculated with coupled cluster response theory. These coupled cluster calculations provide us with an accurate estimate of the lowest... 

These frequencies (calculated with a = 109.5°, w = 12 atomic mass units and / = 5 N/cm) are shown in Fig. 2.5-6. It demonstrate.s that a connection of several similar oscillators to form chains results in exactly as many chain frequencies as there are equal coupled bonds. Although infinitely long chains exhibit infinitely many chain vibrations, only the highest and the lowest of these frequencies are visible in the optical spectra. For long chains, the upper and lower frequency limits (for / = 1 and n 1, respectively) approach the values given by Eq. (2.5-6). Indeed, only the lowest and highest of these frequencies are observed in the infrared and Raman spectra of macromolecules. 

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