FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 1Versuch 3Vertiefungsfach Theoretische ChemiePraktikum im Sommersemester 2011T:2011-04-26Hydrogen Bond in the Water Dimer: Size Consistency Problem and Basis SetSuperposition error.Hydrogen bonds are attractive interactions between a proton donor (X–H) and a protonacceptor (Y) in the same or in a different molecule:X–H · · · YUsually, X and Y are electronegative atoms, although C–H can also be involved in Hydrogenbonds. Hydrogen bonds are, for instance, responsible for the three- dimensional structures ofice, the environment of a water molecule in liquid water and of biomolecules and for the highboiling points of alcohols.Goals:• Characterizing Hydrogen Bonds (binding energies, frequency shifts...)• Investigation of the Size Consistency Problem• Investigation of the Basis Set Superposition ErrorProcedure:First optimize the structures of the monomer and dimer at HF/3-21G level of theory. Suitablestarting geometrical parameters for the dimer are given below. After the geometry optimizations,perform a frequency calculation in order to check that the stationary points that youhave found correspond to minima. Once both minima are located:1. Record their energies with and without ZPVE.2. Report the final geometries.3. Make a brief analysis of the vibrational spectra. Take note of the harmonic vibrationalfrequencies and describe the normal modes associated to them.In order to characterize the strength of the Hydrogen bond present in the dimer, report:1. The binding energy with and without including the ZPVE, defined as D = E[(H 2 O) 2 ]−2 · E[H 2 O].2. The main changes in the geometry of the water molecule which acts as a donor withinthe dimer, with respect to the monomer.
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 23. The main shifts in the vibrational frequencies of the donor in the dimer with respect tothe ones in the monomer.Comment on the following points:How does the inclusion of the ZPVE affect the binding energy? Are the bending and thestretching normal modes of the water molecule which acts as donor in the dimer red or blueshifted with respect to the monomer? What do these facts imply? How does this correlatewith the changes in the geometries on going from the monomer to the dimer?Our next goal is to investigate the effect of the size consistency problem and the basis setsuperposition error in the binding energy.Size consistencySize consistency is defined as the existence of proportionality between the energy of a systemand the number of particles that constitute it. In other words, a certain method is said to besize consistent when the energy of a system A–B, where A and B are infinitely separated, isequal to the sum of A and B energies independently calculated, that is,E (A − B) R=∞= E (A) + E (B)In order to examine this property recalculate single point energies using CISD and CCSDlevels of theory for the monomer and the dimer for a distance between the two monomers d= 50 Å. Are these two methods size consistent? Discuss your results. Discuss the size of theDavidson correction with respect to the total dissociation energy.Basis Set Superposition ErrorThe use of finite basis sets for the calculation of binding energies has implicit the so-calledbasis set superposition error (BSSE). This error has its origin in the better description, andconcomitant stabilization of the fragments A and B in the complex AB, with respect to thecalculation of the two fragments separately. This is due to the fact that in the complex, A andB are better described since the basis functions of the other monomer are also present. Whenthe basis set used for the calculation is big enough so that the addition of more basis functionsdoes not result in a better description of the system, the BSSE is no longer significant. In thosecases where the use of such kind of basis sets is not possible, this error is usually correctedthrough the counterpoise method:BSSE = E[A(B)] + E[B(A)] − E[A] − E[B]Where E [A(B)] represent the energy of monomer A including its basis functions together withthose of monomer B but considering the nuclear charge of the latter as zero and not takinginto account its electrons. Similarly, E[B(A)] is the energy of monomer B in the presence ofthe basis functions of A, considering the nuclear charge of A to be zero and no electrons inthis monomer. E[A] and E[B] represent the energies of monomers A and B.
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 3For making the nuclear charge of an atom zero, use the keyword massage in the input line.At the end of the input write the following for every atom of the dimer whose nuclear chargeyou want to suppress:X NUC 0.0Y NUC 0.0Z NUC 0.0 ...(X, Y, Z... stands for the position of the atom in the Z-matrix)Calculate the BSSE for the HF/3-21G and the CISD/3-21G levels of theory. Discuss the sizeof the BSSE with respect to the total dissociation energy. Suggest a procedure to decreasethis error.Water dimer initial Z-matrix:OH 1 r1H 1 r2 2 a2O 2 r3 1 a3 3 d3H 4 r4 2 a4 1 d4H 4 r5 2 a5 1 d5r1 0.97r2 0.97r3 1.80r4 0.97r5 0.97a2 108.0a3 175.0a4 110.0a5 110.0d3 180.0d4 300.0d5 60.0