Benson and Buss originated the  BGIT in a 1958 article. Within this manuscript, Benson and Buss proposed four approximations: 
# A limiting law for additivity rules.
# Zero-order approximation. Additivity of atomic properties.
# First-order approximation. Additivity of bond properties.
# Second-order approximation. Additivity of group properties.
These approximations account for the atomic, bond, and group contributions to heat capacity (C), enthalpy (ΔH°), and entropy (ΔS°). The most important of these approximations to the group-increment theory is the second-order approximation, because this approximation "leads to the direct method of writing the properties of a compound as the sum of the properties of its group".
The second-order approximation accounts for two molecular atoms or structural elements that are within relative proximity to one another (approximately 3–5 ångstroms as proposed in the article). By using a series of disproportionation reactions of symmetrical and asymmetrical framework, Benson and Buss concluded that neighboring atoms within the disproportionation reaction under study are not affected by the change.
; Symmetrical
; Asymmetrical
In the symmetrical reaction the cleavage between the CH in both reactants leads to one product formation.  that the neighboring carbons are not changed as the rearrangement occurs. In the asymmetrical reaction the hydroxyl–methyl bond is cleaved and rearranged on the ethyl moiety of the methoxyethane. The methoxy and hydroxyl rearrangement display clear evidence that the neighboring groups are not affected in the disproportionation reaction.
The "disproportionation" reactions that Benson and Buss refer to are termed loosely as "radical disproportionation" reactions. From this they termed a "group" as a polyvalent atom connected together with its ligands. However, they noted that under all approximations ringed systems and unsaturated centers do not follow additivity rules due to their preservation under disproportionation reactions. A ring must be broken at more than one site to actually undergo a disproportionation reaction. This holds true with double and triple bonds, as they must break multiple times to break their structure. They concluded that these atoms must be considered as distinct entities. Hence we see C and C groups, which take into account these groups as being individual entities. Furthermore, this leaves error for ring strain, as we will see in its limitations.
From this Benson and Buss concluded that the ΔH of any saturated hydrocarbon can be precisely calculated due to the only two groups being a methylene [C−(C)(H)] and the terminating methyl group [C−(C)(H)]. Benson later began to compile actual functional groups from the second-order approximation. Ansylyn and Dougherty explained in simple terms how the group increments, or Benson increments, are derived from experimental calculations. By calculating the ΔΔH between extended saturated alkyl chains (which is just the difference between two ΔH values), as shown in the table, one can approximate the value of the C−(C)(H) group by averaging the ΔΔH values. Once this is determined, all one needs to do is take the total value of ΔH, subtract the ΔH caused by the C−(C)(H) group(s), and then divide that number by two (due to two C−(C)(H) groups), obtaining the value of the C−(C)(H) group. From the knowledge of these two groups, Benson moved forward obtain and list functional groups derived from countless numbers of experimentation from many sources, some of which are displayed below.