Basis Set Superposition Error (BSSE)
In a combining reaction: A + B => C, the electronic energy change can be calculated using familiar formula: E(C) - (E(A) + E(B)); in which all species are considered at the same level of theory. However, in computational calculations, the product C consists of A and B molecular fragments giving rise to the fact that C inherits a phase bases combined from two sets of primitive functions of A and B with many new integrals appear. This results the fact that C is lower in energy than it really is as referring to the reference energy of reactant well (A and B). This phenomena is sometimes called borrowed basis set, and the arisen error is the "Basis Set Superposition Error (BSSE)" The counterpoise calculation help to correct such error.
- Here we elucidate steps to calculate hydrogen bonding electronic energy of water: H2O + H2O => H2O...H2O at the theoretical level of B3LYP/6-31G(d):
- Analysis: the product is a dimer water borrow basis set from two molecular fragments. Each fragment in the dimer should be located and marked. Optimize all species at the B3LYP/6-31G(d) level. Use optimized geometry of dimer to set input for counterpoise correction:
- Open the dimer output file by GaussView. In View tab, choose Label. The first fragment includes set of atom #1,2,3 and the second one #4,5,6.
- From GassView, choose Edit => Atom List. Highlight atoms of the second fragment (to see if manipulated atoms is correctly belong to the second fragment), and set #2 in the Gaussian Fragment tab.
- Save file and set input file with keyword of counterpoise=2.
# B3LYP/6-31G(d) countepoise=2
Title Card Required
0 1 0 1 0 1
O(Fragment=1) -1.38994389 -0.12369108 -0.10907897
H(Fragment=1) -1.24220750 0.02800549 -1.04543473
H(Fragment=1) -1.90618392 0.59933806 0.25468619
H(Fragment=2) -2.10434580 -1.36111307 0.06985319
O(Fragment=2) -2.58061384 -2.18606124 0.18913972
H(Fragment=2) -3.42541682 -2.13625554 -0.26410119
- With normally terminated job, the BSSE can be found by issuing a command like:
grep "BSSE energy" dimer.out. Result is something like:
Counterpoise: BSSE energy = 0.019154309097