The second heat capacity virial coefficients for argon, carbon dioxide, water, n-pentane, n-octane, and l-propanol were determined from precise isochoric heat capacity measurements from our previous publications in the temperature ranges: argon, between 148 K and 201 K; carbon dioxide, 348 K and 453 K; water, 578 K and 1024 K; n-alkanes, 473 K and 693 K; and l-propanol, 520 K and 690 K. The results were compared with values calculated from recommended density virial coefficients equations and an improved combined spherical symmetric potential function. Values of the second temperature derivatives T(2)d(2)B/dT(2) derived from C-V,C-m measurements for argon, n-pentane, and n-octane were compared with values reported by other authors from C-p,C-m measurements. A new method was developed to calculate second density virial coefficients from caloric (heat capacity) measurements. This method provided the conversion of heat capacity to density second virial coefficients. This paper also describes a new improved combined spherical symmetric model intermolecular potential and a second density virial coefficient equation. The new potential function consists of a repulsive barrier and an attractive square well. Over large distances, it is proportional to r(-6). The parameters of the interaction potential for noble gases (Ar, Ne, Kr, Xe), carbon dioxide, water, n-alkanes (n-C5H12 and n-C8H18), ammonia, and l-propanol were determined from experimental second density virial coefficients. This potential describes second density virial coefficients B(T) within their experimental uncertainties over a wide temperature range.