We present a new approach towards electroweak quantum chemistry including the parity violating weak nuclear force. After introducing the ground work of electroweak quantum chemical perturbation theory to calculate parity violating potentials, E-pv, we present specifically a CIS-RHF method (configuration interaction singles-restricted Hartree-Fock). The method is compared to the previously established and widely used SDE-RHF method for calculations of E-pv [single determinant excitations-restricted Hartree-Fock, R. A. Hegstrom, D. W. Rein, and P. G. H. Sandars, J. Chem. Phys. 73, 2329 (1980)]. It is demonstrated that the new CIS-RHF method can lead to values of E-pv which are more than an order of magnitude larger than those obtained with SDE-RHF (for example in H2O2, where the new maximum value is E-pv= 3.7 x 10(-19)E(h)), Furthermore, the importance of the tensor character of E-pv is outlined by showing that the components of the trace of this tensor E-pv(xx) + E-pv(yy) + E-pv(zz) = E-pv evolve essentially independently from each other in magnitude and sign as functions of molecular structure and computational method. The total Epv results thus as a remainder after substantial mutual cancellation of these components. This finding explains the phenomenon of zero total Epv at chiral geometries, whereas the individual tenser components remain nonzero. We present systematic investigations of parity violating potentials as a function of structure for H2O2, H2S2, N2O4, C2H2, C2H4, C2H6, CH4, and alanine. The effect of nuclear charge Z is investigated for the pair H2O2 and H2S2 and a power law Z(3+delta) (delta approximate to 1.5) for the enhancement of E-pv(ii) can be established with significance for the individual tenser components (i = x,y, or z), whereas just considering the total E-pv would be misleading in analyzing the Z dependence. Contributions of hydrogen atoms to E-pv are estimated and found to be orders of magnitude lower than those of the heavier atoms mentioned. The results are discussed in relation to a possible spectroscopic experiment to measure Delta E-pv = 2E(pv) in enantiomers of chiral molecules and in relation to various hypotheses for the origin of nature of homochirality in chemical evolution.