In this work, rigorous prescreening conditions for the calculation of Franck-Condon factors (FCFs) are derived and implemented. These factors play an important role in numerous applications including the prediction and simulation of vibronic spectra, electron transfer rates, and nonradiative transition probabilities. For larger systems it is crucial to calculate only relevant FCFs, as the computational burden becomes otherwise prohibitive due to the sheer number of Franck-Condon integrals. By exploiting rigorous prescreening criteria one can significantly reduce the computational effort and systematically refine results to the desired target accuracy. In this work, such criteria are derived via the use of sum rules obtained through a coherent state generating function for the FCFs in the harmonic oscillator approximation, following the prescription of Doktorov et al. These sum rules allow efficient and rigorous prescreening prior to the calculation of entire batches of Franck-Condon integrals, reducing the subsequent computational burden. To illustrate the benefit of employing such conditions, they are applied in this work to calculate FC profiles for vibronic spectra of formic acid, thymine, anthracene, and a polycyclic aromatic hydrocarbon derivative containing about 450 vibrational degrees of freedom. Since the prescreening step gives stringent upper and lower bounds for the loss of FC intensity in these spectra arising from the neglected FCFs, the present approach renders most previous a priori selection schemes obsolete and has the potential to complement or even replace other approximate treatments.

In this work a two-component density functional theory study of parity violation induced vibrational frequency shifts in chiral poly-halomethanes is reported and the prospects in these compounds to detect for the first time signals of parity violation in molecular systems are discussed. The recent synthesis and enantiomeric enrichment of CHClFI has renewed interest in examining electroweak corrections for this class of compounds. Utilising a (quasi-relativistic) two-component zeroth-order regular approximation approach to molecular parity violation together with density functional theory, parity violation induced relative vibrational frequency splittings ∆νpv/ν between the C-F stretching fundamental of polyhalomethane enantiomers are computed. The relative splitting in CHClFI is raised compared to CHBrClF, for which upper bounds were determined experimentally. Given these bounds, however, the increase of the relative splitting is not sufficient. Instead the chiral methane derivative CHAtFI is considered which exhibits a significantly larger electroweak correction that induces vibrational frequency splittings on the order of the experimental resolution previously reported for CHBrClF. Employing compounds containing heavy nuclei such as astatine may, thus, be a necessity with present detection methods.

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The projected Hartree-Fock wavefunctions are recast within the framework of the coupled cluster approach. Instead of state projection we directly symmetry adapt the broken symmetry correlation operator via the group invariant mean. The algebraic form for the cluster amplitudes is connected to the underlying symmetry group by this analytical projection, resulting in the inclusion of symmetry structured correlation effects into the wavefunction. After truncating the corresponding cluster amplitudes to a given order, equations that exploit this sparsity can be derived through the bivariational functional of the normal coupled cluster method. This prescription fills in a methodological gap in the standard couple cluster hierarchy, providing an additional means to incorporate pairing and higher order amplitude contributions.