Completely soft molecular electrostatic potentials (CoSMEP) and total density functions

Soft molecular electrostatic potentials (SMEP or SEMP) have been recently defined substituting the point-like proton by a Gaussian positive charge distribution. In the present paper an additional step is taken forward, transforming SMEP into a completely soft MEP (CoSMEP). Such transformation is carried out using a charge distributed proton as in SMEP and also a Gaussian positive nuclear charge distribution, instead of the classical point-like nuclear charges. The general form of MEP is roughly preserved, but new features can be noticed. Such new point of view is also associated to the possibility to redefine the molecular charge density. Definition of CoSMEP is thus connected to the definition of total molecular density functions (DF), where to the negative electronic DF is summed up the soft nuclear DF, made of linear combinations of Gaussian distributions of nuclear charges.