Taking the gas-phase value (no cav.) as the reference, the CASSCF energy obtained with a 10.0 au cavity radius is higher. This is an effect of the repulsive potential, meaning that the molecule is too close to the boundaries. Therefore we discard this value and use the values from 11.0 to 16.0 to make a simple second order fit and obtain a minimum for the cavity radius at 13.8 au.
Once we have this value we also need to optimize the position of the
molecule in the cavity. Some parts of the molecule, especially those
with more negative charge, tend to move close to the
boundary. Remember than the sphere representing the cavity has
its origin in the cartesian coordinates origin. We use the radius of
13.8 au and compute the CASSCF energy at different displacements
along the coordinate axis. Fortunately enough, this molecule has
C
Fitting these values to a curve we obtain an optimal displacement of -1.0 au. We move the molecule and reoptimize the cavity radius at the new position of the molecule. The results are listed in Table .
There is no significant change. The cavity radius is then selected as 13.8 au and the position of the molecule with respect to the cavity is kept as in the last calculation. The calculation is carried out with the new values. The SCF or RASSCF outputs will contain the information about the contributions to the solvation energy. The CASSCF energy obtained will include the reaction field effects and an analysis of the contribution to the solvation energy for each value of the multipole expansion:
## 10.6.4 Solvation effects in ground states. PCM model in formaldehyde.
The reaction field parameters are added to the
To invoke the PCM model the keyword
is required. A possible input is
which requests a PCM calculation with acetone as solvent, with tesserae
of average area
. Note that the default parameters are
solvent=water, average area
; see the A complete input for a ground state CASPT2 calculation on formaldehyde () in water is
## 10.6.5 Solvation effects in excited states. PCM model and acrolein.
In the PCM picture, the solvent reaction field is
expressed in terms of a polarization charge density spread
on the cavity surface, which, in the most recent version of the method,
depends on the electrostatic potential
generated by the solute on the cavity according to
where is the solvent dielectric constant and is the (electronic+nuclear) solute potential at point on the cavity surface. The and operators are related respectively to the electrostatic potential and to the normal component of the electric field generated by the surface charge density . It is noteworthy that in this PCM formulation the polarization charge density is designed to take into account implicitly the effects of the fraction of solute electronic density lying outside the cavity. In the computational practice, the surface charge distribution is expressed in terms of a set of point charges placed at the center of each surface tessera, so that operators are replaced by the corresponding square matrices. Once the solvation charges ( q) have been determined,
they can be used to compute energies and properties in solution.
The interaction energy between the solute and the solvation charges can be written
V_{i} is the solute potential calculated at the representative point
of tessera i. The charges act as
perturbations on the solute electron density : since the charges
depend in turn on through the electrostatic potential, the solute
density and the charges must be adjusted until self consistency.
It can be shown[261] that for any SCF procedure including a
perturbation linearly depending on the electron density,
the quantity that is variationally minimized corresponds to a free energy
(i.e. E_{int} minus the work spent to polarize the dielectric and to create
the charges).
If
is the solute energy in vacuo, the free energy
minimized in solution is
V_{NN} is the solute nuclear repulsion energy, is the
solute electronic density for the isolated molecule, and is the
density perturbed by the solvent.
The inclusion of non-equilibrium solvation effects, like those occurring during electronic excitations, is introduced in the model by splitting the solvation charge on each surface element into two components: q_{i,f} is the charge due to electronic (fast) component
of solvent polarization, in equilibrium with the solute electronic density
upon excitations, and q_{i,s}, the charge arising from the orientational
(slow) part, which is delayed when the solute undergoes a sudden transformation.
The photophysics and photochemistry of
acrolein are mainly controlled by the relative position of the
, and states, which is,
in turn, very sensitive to the presence and the nature of the solvent.
We choose this molecule in order to show an example of how to
use the PCM model in a CASPT2 calculation of vertical excitation
energies.
The three states we want to compute are low-lying singlet
and triplet excited states of the
If not specified, the default solvent is chosen to be water.
Some options are available. The value of the dielectric constant
can be changed for calculations at temperatures other than 298 K.
For calculations in polar solvents like water, the use of the conductor
model (C-PCM) is recommended.
This is an approximation that employs conductor rather than dielectric
boundary conditions. It works very well for polar solvents
(i. e. dielectric constant greater than about 5), and is based
on a simpler and more robust implementation. It can be useful also in cases when
the dielectric model shows some convergence problems.
Another parameter that can be varied in presence of convergency problem
is the average area of the tesserae of which the surface of the cavity is composed.
However, a lower value for this parameter may give poorer results.
Specific keywords are in general needed for the other modules to work with PCM, except for
the SCF. The keyword RFpert must be included in the CASPT2 input
in order to add
the reaction field effects to the one-electron hamiltonian as a constant perturbation.
Information about the reaction field calculation employing a PCM-model appear first in the SCF output
The following input is used for the CASPT2 calculation of the
state.
Provided that the same $WorkDir has been using, which contains all the files of of the
calculation done for the ground state, the excited state calculation is done
by using inputs for the calculations:
CASPT2
Note the ).
SEWARD
The
This piece of information means that the program computes the solvent effects on the energy of the by using a non-equilibrium approach. The slow component of the solvent response is kept frozen in terms of the charges that have been computed for the previous equilibrium calculation of the ground state. The remaining part of the solvent response, due to the fast charges, is instead computed self-consistently for the state of interest (which is state 1 of the specified spatial and spin symmetry in this case).
The vertical excitations to the lowest valence states
in aqueous solution for No experimental data are available for the excitation energies to the triplet states of acrolein in aqueous solution. However it is of interest to see how the ordering of these two states depends on solvent effects. The opposing solvatochromic shifts produced by the solvent on these two electronic transitions place the two triplet states closer in energy. This result might suggest that a dynamical interconversion between the and may occur more favorable in solution.
Next: 10.7 Computing relativistic effects
Up: 10. Examples
Previous: 10.5 Excited states.
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