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					Lab 12.      Solvation

In all of the calculations that we have done up to this point, the molecules and atoms were isolated (e.g., in a vacuum). Such
calculations provide a good approximation to a molecule in the gas phase. However, sometimes the solvent may play an
important role in structure, reaction energies and many other issues of chemical importance. The question is, how to include the
                                       influence of the solvent? Including millions of solvent molecules in a calculation is
                                       typically not feasible. The wide range of models used to approximately include the
                                       influence of solvation in molecular calculations usually fall into one of two main classes:
                                       explicit solvent molecules and contiuum models. In this lab, we will use the latter models.

                                      Often a solvent molecule will not bond directly to the molecule of interest, or participate
                                      directly in a reaction that is under investigation. The solvent can still be influential
                                      however, by stabilizing a product, reactant, or transition state. Solvent molecules will have
                                      a dipole moment or at least be polarizable. These dipolar or polarizable species will
                                      interact with and stabilize the charge build up in a molecule. A solvent may then affect the
                                      structure and properties of a molecule through this interaction, particularly if the solvent
                                      and/or molecule are particularly polar. How a solvent will influence the progress of a
reaction is difficult to predict ahead of time because the solvent will interact differently with the reactants, products,
intermediates and transition states of that reaction. Also, solvents of different dielectric will interact differently. Including this
“dipole/polarizable medium” interaction in a calculation through the addition of discrete solvent molecule is difficult because in
order to do a reasonable job a very large number of solvent molecules must be included. An alternative approach is to use a
“continuum model” of the solvent. Coninuum solvation models are still an area of active research.What is meant by “continuum
model” is that we describe the solvent as a single continuous blob with appropriate electrostatic properties rather than as
isolated molecules. The solvation is achieved by digging an appropriately sized hole out of the solvent medium as represented
by a single dielectric, putting the molecule into the hole, and allowing the electrons and nuclei of the molecule to interact with
the solvent medium. Numerous different continuum models exist. The differences between each of these models depend on the
technical details of the approach within the quantum mechanical ansatz. A few choices can be made about how the solvent
medium should be represented, choices about how to define the cavity that represents the boundary between the solute and the
solvent, how to represent the solute in that solvent, and how to make the mutual interaction self consistent within the SCF
procedure. Each continuum model contains some parameters, for example the dielectric of the solvent, orrepresentaton of the
cavity.


Exercise 1. Effect of Cavity Size and Shape

Molecule: H2O
Level of Theory: B3LYP/6-31G(d)
Calculations to run:
      1. Run a Gas phase H2O optimization using an input as in the example below.
               a. Record the O-H bond distance, the dipole, and the final energy
               b. If you were to estimate a spherical cavity for the water molecule, what would you predict the radius of the
                    sphere to have to be in order to fully encompass the single H2O molecule? [Look carefully at the geometry
                    and estimate based on that geometry]


                                   $contrl scftyp=rhf runtyp=optimize coord=zmt $end
                                   $basis gbasis=sto ngauss=3 $end
                                   $guess guess=huckel $end
                                   $data
                                   water in water, arbitrary geometry
                                   Cnv 2

                                   O
                                   H 1 rOH
                                   H 1 rOH 2 aHOH

                                   rOH = 0.95
                                   aHOH = 104.5
                                    $end
      2. Solvent calculation using the Onsager spherical cavity model
             a. Take the optimized gas phase geometry, and update the gas phase H2O input with the new geometry, and
                 save this input with a new name (H2O_onsager.inp). Add this additional line to your input, replacing X.XX
                 with the radius that you predicted in part 1b.
                               $scrf radius=X.XX dielec=80.0 $end
             b. Run the calculation and record the O-H bond distance, the dipole, and the final solvated energy.
             c. Calculate the solvation energy: [E(gas phase) – E(solution phase)]*627.517 (kcal/mol).
             d. Run the same calculation using cavity radii that is a) smaller than the size of the molecule, and b) much
                 larger than the size of the cavity. Calculate the solvation energies.
      3. Solvent calculation using the PCM continuum solvation model (Molecular shaped cavity)
             a. Take the input H2O_onsager.inp and replace the $scf line with the following line, which will enable us to do
                 a more accurate molecular-shaped cavity solvation calculation using the polarized continuum model (PCM).
                               $pcm solvnt=water $end
             b. Run the calculation and record the O-H bond distance, the dipole, and the final solvated energy.
             c. Calculate the solvation energy: [E(gas phase) – E(solution phase)]*627.517 (kcal/mol).

       Compare your results to the experimental solvation energy value of -6.29. Comment on the importance of a realistic
cavity construction for such computations. What is the biggest problem associated with using a spherical cavity? Can you
think of a molecule where the spherical cavity would be appropriate? Can you think of a molecule where a spherical cavity
would not be appropriate?

Exercise 2. Effect of solvation on structure and properties.

Molecules: formaldehyde
Level of theory: RHF/6-31+G(d)
Additional Information: See Lab 7, Stretching frequency Exercise, Formaldehyde

      1. Take the input used in Lab 7 for formaldehyde and change the key words in $CONTRL and $BASIS to match the
         following in order to carry out a new gas phase optimization at the level written above. Record the carbon-oxygen
         bond length and the dipole. Take the optimized coordinates and run a HESSIAN to obtain the frequencies. Record
         the frequencies.

 $CONTRL SCFTYP=RHF RUNTYP=optimize $END
 $BASIS GBASIS=N31 NGAUSS=6 NDFUNC=1 NDIFFS=.t. $END
 $GUESS GUESS=HUCKEL $END
$DATA
formaldehyde
cnv 2

 CARBON           6.0     0.0000000000         0.0000000000       -1.1286765958
 OXYGEN           8.0     0.0000000000         0.0000000000        0.0496420580
 HYDROGEN         1.0    -0.9276466617         0.0000000000       -1.7104827311
 $END


      2.   Next, using the optimized gas phase geometry, we will carry out a solution phase calculation in acetonitrile, with
           dielectric 35.7, as in this next input:

 $CONTRL SCFTYP=RHF RUNTYP=optimize $END
 $BASIS GBASIS=N31 NGAUSS=6 NDFUNC=1 DIFFSP=.t. $END
 $cosgms epsi=35.9 $end
 $GUESS GUESS=HUCKEL $END
 $DATA
formaldehyde
cnv 2

CARBON        6.0 0.0000000000 0.0000000000 -1.1336519500
OXYGEN        8.0 0.0000000000 0.0000000000 0.0522318206
HYDROGEN 1.0 -0.9264028589 0.0000000000 -1.7092899353
$end

       Record the carbon-oxygen bond length and dipole, and calculate the solvation energy for formaldehyde in acetonitrile.
       Take the optimized coordinates and run a HESSIAN analysis to obtain the frequencies in solution. Record the
       frequencies obtained.

Compare your results to the experimental value in the following table:

Model                         A        A       A       
Gas phase
Expt           1167           1249           1500            1746           2782           2843

PCM
Expt                          1247           1503            1723           2797           2876

Another useful way of looking at this data is to compute the frequency shifts in going from gas phase to acetonitrile:


Model                       A       A      A      
PCM-GP
Expt                          -2             +3              -23            +15            +33

What conclusions can you draw?

				
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posted:9/27/2012
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