# Water Dimer Results

### PURPOSE:

Examine the water dimer system to determine what level of theory is necessary to determine the PES with chemically useful accuracy.

### RESULTS:

*Tools:*

All Hartree-Fock and Moller-Plesset (MP) results were calculated using the PC GAMESS version [1] of the GAMESS (US) QC package [2] . Density Functional results were calculated using Gaussian 98W [3].

*Methods:*

Results were calculated using standard methods (i.e. Hartree-Fock (HF) and HF with correlation corrections from Moller-Plesset perturbation theory (MP2, MP3, MP4 SDQ, and MP4 SDTQ)). For all the MP calculations we used the entire space of occupied and virtual orbitals for the calculation. No orbitals were omitted. We also used two Density Functional methods (B3LYP and MPW1PW91) which explicitly include correlation effects at the SCF level of calculation.

1) Basis Sets

All basis sets used in this study were obtained from the Extensible Computational Chemistry Environment Basis Set Database [4]. Gaussian 98 basis sets were specified using the 6D 10F option to ensure basis set equivalence between the PC GAMESS and Gaussian calculations. Using the knowledge from our Neon analysis, all basis sets contain augmenting diffuse functions. The specific basis sets used (listed in terms of increasing completeness) were:

Click on the Designation for complete basis set information.

2) Linear Independence

Linear dependence problems can occur when using very large Cartesian gaussian basis sets augmented with many diffuse functions. The problem arises from the presence of linear combinations of Cartesian gaussian functions that are equivalent to other functions in the basis set (e.g. X2+Y2+Z2 is equivalent to an S type function). This equivalence violates the basic assumption that the basis set consists of a sum of functions that are independent of each other.

In this case, the problem was initially observed at the AUG-cc-pVQZ basis and required the removal of one s-type function (exponent value of 0.2067) from each Oxygen atom. Calculations were attempted using Dunning's AUG-cc-pV5Z basis but extensive linear dependence problems were observed. All attempts at their resolution resulted in basis sets that differed only marginally from the AUG-cc-pVQZ basis so these calculations were not performed.

3) Binding Energy Definition

The PESs are calculated from the Binding Energy at various geometrical configurations of the two water molecules. Binding Energy (BE) is defined as:

BE(counterpoise)= Energy(dimer)

**-** Energy(water1 + basis set of water2 (located at water2's position))

**-** Energy(water2 + basis set of water1 (located at water1's position))

Our definition of Binding Energy takes into account basis set superposition errors (BSSE). These errors arise from the fact that there are more basis functions used to represent the combined system than there are to represent the individual components. See our Neon results for more details. Note: throughout the rest of this document we will refer to this method of binding energy calculation as double counterpoise or DCP.