| The topic of solvatochromism — and
the various models available to implement solvatochromic effects into
excited-state calculations — is one that is complex because (as touched
upon in some of the discussion that prompted this
post),
(i) there are at least two solvent response time
scales that need to be considered for vertical processes, (ii) there
are many quite different means to determine excited-state wave functions, or
response properties, (iii) for those models based on a
ground-state reference, one can adopt varying degrees of self-consistency with
respect to the excited state for each (all) of the various operators involved,
and finally (iv) there may or may not be enforcement of orthogonality
between the solvated excited state and the solvated ground
state
Those interested in this topic may find our paper
— Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.; Guido, C. A.; Mennucci,
B.; Scalmani, G.; Frisch, M. J. "Practical Computation of Electronic Excitation
in Solution: Vertical Excitation Model" Chem. Sci. 2011, 2,
2143 (doi:10.1039/c1sc00313e) — useful in so far as Table 2 attempts
to systematically categorize various solvation models (including those
implemented into Gaussian 09) with respect to the manner in which they address
these various issues. There is, of course, accompanying discussion that goes far
beyond anything I’d want to blast to all of
CCL...
Best regards,
Chris
Cramer Dear Mr. DiFan,
We had recently a wonderful
conversation on this topic with Gaussian help center (which I would always
advice You to contact, help{}gaussian.com), so I post here some quotes > from their
thorough reply (saving therefore some time for them :) ). I hope You will find
something useful in these quotes. In regular TD-SCF calculations one is using a linear
response approach. One computes the ground state reference (SCF) and the solvent
reaction field self-consistently with each other. Starting from that
self-consistent reaction field in equilibrium with the ground SCF electron
density, the linear-response approach add extra solvation terms that provide
correction for solvation effects on the excited state energies and properties.
This is an approximation to a self-consistent approach for solving the solvent
reaction field in equilibrium with the excited state density (such as
"ExternalIteration"). These solvation effects via "linear response" approach are
computed at each geometry, so they are being updated in a TD-SCF geometry
optimization, they are not frozen > from the first optimization step.
The
way you can think about the difference between "linear-response" and
"externaliteration" is that "linear-response" apply the solvation effects to the
transition electric dipole, while "externaliteration" reflects the difference in
solvation effects between excited and ground states. Thus, "linear-response" is
going to work reasonably well for "bright", "dipole allowed" electronic
transitions. For "dark", "dipole forbidden" electronic transitions, the
transition electric dipoles are going to be zero or almost zero, so the
solvation effects computed with a "linear response" approach are going to be
negligible. This may be correct if the excited and ground states have similar
dipole moments, therefore similar electrostatic interactions with the solvent.
However, if excited and ground states have noticeably different dipole moments,
the solvation effects on the excitation energies can also be significant and the
"linear response" approach would not be able to capture that solvation effect,
while the "externaliteration" approach may be able to do a better
job.
--------
The response of the solvent to a change in the electron
density of the solute is generally separated into two components, "slow" and
"fast". In a photon absorption process, one can assume that there is a fast
change in the solute electron density as a result of the absorption and that the
relaxation of the solute geometry and the solvation shell around the solute
occurs much slower than the initial change in the solute electron density. So,
when modeling a photon absorption process, we would want to allow the "fast"
(electronic) component of the solvent polarization to respond to the change in
the solute electron density, while keeping the "slow" (orientational) component
of the solvent polarization frozen from what was in equilibrium with the ground
state electron density. What I described is a "non-equilibrium" solvation
process and this is the default for TD-SCF single point energy calculations with
SCRF, since typically one does a TD-SCF single point energy calculation at the
optimized ground state geometry in order to obtain ground to excited state
vertical excitation energies to model a photon absorption
process.
Calculations of the TD-SCF excited state relaxed density
(Density=Current), geometry optimizations, and frequency calculations are done
by default as "equilibrium" solvation processes, so both the the "fast"
(electronic) and "slow" (orientational) components of the solvent polarization
are allowed to respond to the change in the solute electron density. It makes
sense since, in an excited state geometry optimization, one is trying to find
the equilibrium geometry, so at the equilibrium geometry the solvent reaction
field should be in equilibrium with the solute excited state.
Note
also that since an "ExternalIteration" job involves the computation of an
excited state density (in order to self-consistently solve the reaction field),
the default for an "ExternalIteration" job is to use an "equilibrium" solvation
process. Therefore, if one wants to use "ExternalIteration" for an absorption
process, for example, i.e. solve only for the "fast" solvent polarization
self-consistently, one would need to specifically run an ground state job saving
the solvent reaction field to the checkpoint file and then run the
"ExternalIteration" job and request a non-equilibrium process by reading the
solvent reaction field from the checkpoint file. There is an example of this in
the documentation of the SCRF keyword in the G09 manual. There is also one
example for the emission process, where one uses equilibrium solvation in the
excited state "ExternalIteration" job at the excited state equilibrium geometry,
and saving the solvent reaction field in equilibrium with the excited state.
Then one needs to run a ground state single point energy calculation requesting
non-equilibirum solvation by reading the solvent reaction field from the
checkpoint file.
Christopher J.
CramerElmore H. Northey Professor and Associate Dean for Academic
Affairs University of Minnesota Department of Chemistry and College of Science &
Engineering Phone: (612) 624-0859 (Chemistry) Phone: (612) 624-9371 (CSE) -------------------------- Mobile: (952) 297-2575 Twitter:
---ChemProfCramer
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