The parameter Wa, which characterizes nuclear-spin-dependent parity violation (PV) in the molecular spin-rotational Hamiltonian, was computed with a quasirelativistic Hartree-Fock approach for radium fluoride (RaF) and found to be one of the largest absolute values predicted so far. The peculiar electronic structure of RaF leads to highly diagonal Franck-Condon matrices between the energetically lowest two electronic states, which qualifies RaF for direct laser cooling. A subset of diatomic molecules with a wide range of internal structures suitable for this cooling technique is also indicated. As trapped cold molecules offer superior coherence times, RaF can be considered promising for high-precision experiments aimed at molecular PV.

A rational approach to identify polyatomic molecules that appear to be promising candidates for direct Doppler cooling with lasers is outlined. First-principles calculations for equilibrium structures and Franck-Condon factors of selected representatives with different point-group symmetries (including the chiral nonsymmetric $C_1$) have been performed and a high potential for laser cooling of these molecules is indicated.

Recently, a few diatomic and polyatomic molecules have been identified as prospective systems for Doppler/Sisyphus cooling. Doppler/Sisyphus cooling allows us to decrease the kinetic energy of molecules down to μ K temperatures with high efficiency and allows their capture in molecular traps, including magneto-optical traps. Trapped molecules can be used for creating molecular fountains and/or performing controlled chemical reactions, high-precision spectra measurements, and a wealth of other applications. Polyatomic molecules with heavy nuclei are of considerable interest for the ‘new physics’ search outside of the Standard Model and other applications including cold chemistry and photochemistry, quantum informatics, etc. Here, we focus on the radium monohydroxide molecule (RaOH), which is on the one hand amenable to laser cooling and on the other hand opens excellent possibilities for  -odd and  ,  -odd effects research. At present, RaOH is the heaviest polyatomic molecule proposed for direct cooling with lasers.

Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of $P$- and $T$-and-$P$–violating interactions. The parameters of $P$- and $T,P$-odd terms of the spin-rotational Hamiltonian have been calculated for the ${}^2\Sigma$ electronic ground state of the ${}^{223}\mathrm{RaF}$ molecule. They include the $W_a$ parameter, which is critical in the experimental search for nuclear anapole moment, and the parameters $W_d$ and $W_{\mathrm{SP}}$ required to obtain restrictions on the electric dipole moment of the electron and $T,P$-odd scalar-pseudoscalar interactions, respectively. The parameter $X$ corresponding to the “volume effect” in the $T,P$-odd interaction of the ${}^{223}\mathrm{Ra}$ nuclear Schiff moment with electronic shells of RaF has also been computed. Spectroscopic and hyperfine structure constants for ${}^{223}\mathrm{RaF}$ and ${}^{223}{\mathrm{Ra}}^{+}$ have been computed as well, demonstrating the accuracy of the methods employed.

We report ab initio relativistic correlation calculations of potential curves for ten low-lying electronic states, the effective electric field on the electron, and hyperfine constants for the ${}^3\Delta _1$ state of a cation of the heavy transition metal fluoride $\mathrm{Hf}{\mathrm{F}}^{+}$, which it is suggested can be used in experiments to search for the electric dipole moment of the electron. It is shown that $\mathrm{Hf}{\mathrm{F}}^{+}$ has a deeply bound ${}^1\Sigma ^{+}$ ground state; its dissociation energy is $D_e=6.4\mathrm{eV}$. The ${}^3\Delta _1$ state is obtained as the relatively long-lived first excited state lying about $0.2\mathrm{eV}$ higher. The calculated effective electric field $E_{\mathrm{eff}}=W_d\mid \Omega \mid$ acting on an electron in this state is $5.84\times {10}^{24}\mathrm{Hz}∕e\mathrm{cm}$.

Photoelectron circular dichroism refers to the forward/backward asymmetry in the photoelectron angular distribution with respect to the propagation axis of circularly polarized light. It has recently been demonstrated in femtosecond multi-photon photoionization experiments with randomly oriented camphor and fenchone molecules [C. Lux et al., Angew. Chem., Int. Ed. 51, 4755 (2012) and C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013)]. A theoretical framework describing this process as (2+1) resonantly enhanced multi-photon ionization is constructed, which consists of two-photon photoselection from randomly oriented molecules and successive one-photon ionization of the photoselected molecules. It combines perturbation theory for the light-matter interaction with ab initio calculations for the two-photon absorption and a single-center expansion of the photoelectron wavefunction in terms of hydrogenic continuum functions. It is verified that the model correctly reproduces the basic symmetry behavior expected under exchange of handedness and light helicity. When applied to fenchone and camphor, semi-quantitative agreement with the experimental data is found, for which a sufficient d wave character of the electronically excited intermediate state is crucial.