Tests for chemical realizability

Test 1. If ( o, i. 2 3) are four immediate neighbors of a carbon atom, then we only accept an abstract POF as candidate if x(ao, , 0- 

This test excludes the only chemically non-realizable POF of example 4.2a. It has no effect on example 4.2b, since there are no such atom quadruples explicitly considered in 4.2b. (We do not care about the hydrogen atoms in this example.) For example 4.2c, we postulate (0,5,6,7) 0 and (1,2,3,4) 0, which reduces the number of candidates generated to 40,095. 

Test 2a. Suppose and 02 are carbon atoms connected by a single bond, is a neighbor of , emd 02 has another three neighbors. Among the neighbors of oj, there is at most one atom 03 with fl2 3) = 

Using this rule on example 4.2c we postulate that e.g. among 1,2,5), (0,1,2,6), and x(.0,1.2,7), there is at most one function with the value zero. Using Tests 1 and 2a, the number of generated candidates for exeunple 4.2c is reduced to 11,368. 

A stronger version of this test is to force at least one atom on one side of the plane defined by atoms oq, i, and aj. and at least one atom on the other side. 

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