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We have developed an analytical approach for computing Franck-Condon integrals (FCIs) of harmonic oscillators (HOs) with arbitrary dimensions in which the mode-mixing Duschinsky effect is taken into account. A general formula of FCIs of HOs was obtained and was applied to study the photoelectron spectroscopy of vinyl alcohol and ovalene (C32H14). The equilibrium geometries, harmonic vibrational frequencies and normal modes of vinyl alcohol, ovalene, and their cations were computed at the B3LYP/aug-cc-pVTZ or the B3LYP/6-31G(d) level, from which Franck-Condon factors were calculated and photoelectron spectra were simulated. The adiabatic ionization energies of vinyl alcohol were also computed by extrapolating the CCSD(T) energies to the complete basis set limit with aug-cc-pVXZ (X = D, T, Q, 5). The simulated photoelectron spectra of both vinyl alcohol and ovalene are in agreement with the experiments. The computed adiabatic ionization energies of syn- and anti-vinyl alcohol are in consistent with the experiment within 0.008 eV and 0.014 eV, respectively. We show, for the first time, that the analytical approach of computing FCIs is also efficient and promising for the studies of vibronic spectra of macrosystems. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

This paper presents the design of a direct-injection divide-by-3 frequency divider operating at the K-band. The divider is implemented in a 0.18-\mu\ m CMOS process. The measured free-running frequency of the divider is 7.96 GHz. By utilizing a floating-source differential injector and without a varactor tuning in the divider core, the total locking range is 3.2 GHz with a power consumption of 8.28 mW from a supply voltage of 0.9 V. The total power consumption of the buffers is 9.54 mW from a supply voltage of 1.8 V. The measured phase noise of the divider is -141.3 dBc/Hz at 1-MHz offset when the input referred signal with a phase noise of -132.8 dBc/Hz at 1-MHz offset from 24 GHz. The phase-noise difference of 8.5 dB is close to the theoretical value of 9.5 dB for division-by-3. The output power of the divider is more than -11 dBm over the whole locking range. [ABSTRACT FROM PUBLISHER]