17 research outputs found
Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems: II. Dipole-dipole versus current-current correlations
Based on Takayama-Lin-Liu-Maki model, analytical expressions for the
third-harmonic generation, DC Kerr effect, DC-induced second harmonic optical
Kerr effect, optical Kerr effect or intensity-dependent index of refraction and
DC-electric-field-induced optical rectification are derived under the static
current-current() correlation for one-dimensional infinite chains. The
results of hyperpolarizabilities under correlation are then compared
with those obtained using the dipole-dipole () correlation. The comparison
shows that the conventional correlation, albeit quite successful for
the linear case, is incorrect for studying the nonlinear optical properties of
periodic systems.Comment: 11 pages, 5 figure
Zero frequency divergence and gauge phase factor in the optical response theory
The static current-current correlation leads to the definitional zero
frequency divergence (ZFD) in the optical susceptibilities. Previous
computations have shown nonequivalent results between two gauges ( and ) under the exact same unperturbed wave functions. We
reveal that those problems are caused by the improper treatment of the
time-dependent gauge phase factor in the optical response theory. The gauge
phase factor, which is conventionally ignored by the theory, is important in
solving ZFD and obtaining the equivalent results between these two gauges. The
Hamiltonians with these two gauges are not necessary equivalent unless the
gauge phase factor is properly considered in the wavefunctions. Both
Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models of
trans-polyacetylene serve as our illustrative examples to study the linear
susceptibility through both current-current and dipole-dipole
correlations. Previous improper results of the calculations and
distribution functions with both gauges are discussed. The importance of gauge
phase factor to solve the ZFD problem is emphasized based on SSH and TLM
models. As a conclusion, the reason why dipole-dipole correlation favors over
current-current correlation in the practical computations is explained.Comment: 17 pages, 7 figures, submitted to Phys. Rev.
Analytical solutions to the third-harmonic generation in trans-polyacetylene: Application of dipole-dipole correlation on the single electron models
The analytical solutions for the third-harmonic generation (THG) on infinite
chains in both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models
of trans-polyacetylene are obtained through the scheme of dipole-dipole ()
correlation. They are not equivalent to the results obtained through static
current-current () correlation or under polarization operator
. The van Hove singularity disappears exactly in the analytical forms,
showing that the experimentally observed two-photon absorption peak (TPA) in
THG may not be directly explained by the single electron models.Comment: 10 pages, 4 figures, submitted to Phys. Rev.
Infrared spectroscopy of small-molecule endofullerenes
Hydrogen is one of the few molecules which has been incarcerated in the
molecular cage of C and forms endohedral supramolecular complex
H@C. In this confinement hydrogen acquires new properties. Its
translational motion becomes quantized and is correlated with its rotations. We
applied infrared spectroscopy to study the dynamics of hydrogen isotopologs
H, D and HD incarcerated in C. The translational and rotational
modes appear as side bands to the hydrogen vibrational mode in the mid infrared
part of the absorption spectrum. Because of the large mass difference of
hydrogen and C and the high symmetry of C the problem is
identical to a problem of a vibrating rotor moving in a three-dimensional
spherical potential. The translational motion within the C cavity breaks
the inversion symmetry and induces optical activity of H. We derive
potential, rotational, vibrational and dipole moment parameters from the
analysis of the infrared absorption spectra. Our results were used to derive
the parameters of a pairwise additive five-dimensional potential energy surface
for H@C. The same parameters were used to predict H energies
inside C[Xu et al., J. Chem. Phys., {\bf 130}, 224306 (2009)]. We
compare the predicted energies and the low temperature infrared absorption
spectra of H@C.Comment: Updated author lis