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1. A common TD job will give the enough information of verticle excitation and emission in gas phase, but a statespecific job need to be run for that in solvation. I want to the function of the statespecific job. £¨ÕâÒ»¾äÊÇÎÒÎʵÄÎÊÌ⣩

The "StateSpecific" approach in this context applies to the excited state, and yes it involves solving self-consistently the "fast" component of the solvent polarization for the target state and non-equilibrium solvation for the "slow" component of the solvent polarization (i.e. the "slow" component of the solvent polarization comes from the origin state).

The total polarization is always partitioned into two components, "slow" and "fast". The "slow" part can be regarded as the reorganization of the solvent molecules as a response to a change in the electronic density of the solute. The "fast" part can be regarded as the response of the electrons in the solvent to a change in the electronic density of the solute. For a change in the electronic density of the solute such as a vertical electronic transition, the "slow" component of the polarization is much slower than the timescale of the electronic transition, so the solvent does not have time to respond in this way to the vertical electronic transition. The "fast" component of the polarization, on the other hand, is closer in timescale to the vertical electronic transition on the solute.

In an equilibrium solvation calculation, both components are in equilibrium with the solute's density. By default, all ground state calculations assume equilibrium solvation, as well as geometry optimizations of excited states (and also any calculation that involves the computation of the relaxed density of the excited state). Again, in equilibrium solvation processes, both the "slow" and "fast" component of the solvent polarization are in equilibrium with the excited state density.

In the case of a TD energy calculation (no excited state density or geometry optimization) for the computation of a vertical electronic excitation, the default is to do a non-equilibrium process. For this case then, the "fast" component of the polarization "responds" to the change in the solute density from ground to excited state, but the "slow" component did not have time to "respond" so it still comes from the one that was in equilibrium with the solute's ground state density. This is the case of both "Step 2" and "Step 3" in the example shown in the manual.

In "Step 2", an energy calculation using TD is performed, thus it defaults to non-equilibrium solvation. The solvation effects on the excited states energies are computed by means of a linear response approach. The absorption energies via the linear response approach only are those reported directly in the output of this "Step 2" job.

In "Step 3", a step further is taken and a correction of the linear response excitation energy is performed by solving the "fast" component of the solvent polarization self-consistently with the selected excited state density (the "State-Specific" approach). This is generally an improvement over the excitation energies obtained by linear response alone. Note that since this "State-Specific" approach involves the calculation of the excited state density, the program would default to doing an equilibrium solvation calculation on the excited state. However, the goal of "Step 3" is to compute the vertical excitation energy, so as mentioned above, we would like to use the "slow" component of the solvent polarization from the ground state calculation (in "Step 3", the first part does an equilibrium calculation on the ground state saving the solvent reaction field to the checkpoint file) and solving self-consistently the "fast" component with the excited state density (the second part of "Step 3" reads the reaction field from the checkpoint file, the one from the ground state calculation, keeps the "slow" component as is, and solves the "fast" component self-consistently with the excited state density). The absorption energy via the "State-Specific" approach is the energy difference between the excited state energy after all PCM corrections from the non-equilibrium calculation in "Step 3" and the ground state energy resulting from the equilibrium process (either first part of "Step 3" or final, optimized geometry, energy from "Step 1", the two ground state energies should be the same).

In a TD geometry optimization of an excited state, since one is looking for the equilibrium geometry, the default is to do equilibrium solvation, so the two components, "slow" and "fast", of the polarization are in equilibrium with the solute's excited state density. All "Step 4", "Step 5" and "Step 6" use equilibrium solvation for the selected excited state.

The emission energy (vertical energy of the excited to ground state transition) by means of a linear response approach can be found in the output of "Step 4". For the final (optimized) geometry in "Step 4", the "excitation energy" shown in this output would be equal to the emission energy since it is the result of an equilibrium calculation on the selected excited state.

"Step 6" and "Step 7" are analogous to the two parts of "Step 3" but this time for the opposite transition (excited to ground states). Thus, "Step 6" is analogous to the first part of "Step 3", it is an equilibrium calculation on the origin state (now the excited state) in which both "slow" and "fast" components of solvent polarization are solved self-consistently with the excited state density (this calculation can be regarded as a correction of the excited state energy beyond the linear response approach, which was done in "Step 4". Now, this "Step 6" saves the solvent reaction field to the checkpoint file. "Step 7" reads this information from the file (just like the second part of "Step 3" and performs a non-equilibrium calculation of the ground state energy, using the "slow" component of the solvent polarization from the excited state calculation ("Step 6" and only doing the "fast" component of the solvent polarization self-consistent with the ground state density. The emission energy via the "State-Specific" approach would be the energy difference between the excited state energy after all PCM corrections from "Step 6" and the ground state energy resulting from the non-equilibrium process in "Step 7".

These are a few relevant references that deal with different aspects of PCM, equilibrium vs. non-equilibrium solvation, solvation effects in electronic transition calculations:

- A review that covers many of the aspects of continuum solvation models (including a section in non-equilibrium):

J. Tomasi, B. Mennucci and R. Cammi, "Quantum Mechanical Continuum Solvation Models," Chem. Rev., 105 (2005) 2999-3093.

- A couple of early references dealing with solvation in electronic transitions:

M. Cossi and V. Barone, ¡°Solvent effect on vertical electronic transitions by the polarizable continuum model,¡± J. Chem. Phys., 112 (2000) 2427-35.

M. Cossi and V. Barone, ¡°Time-dependent density functional theory for molecules in liquid solutions,¡± J. Chem. Phys., 115 (2001) 4708-17.

- A couple of references related to the State-Specific (or external iteration) treatment of solvation in electronic transitions:

R. Improta, V. Barone, G. Scalmani, and M. J. Frisch, ¡°A state-specific polarizable continuum model time dependent density functional method for excited state calculations in solution,¡± J. Chem. Phys., 125 (2006) 054103.

R. Improta, G. Scalmani, M. J. Frisch, and V. Barone, ¡°Toward effective and reliable fluorescence energies in solution by a new State Specific Polarizable Continuum Model Time Dependent Density Functional Theory Approach,¡± J. Chem. Phys., 127 (2007) 074504.

2. For seven example steps in the guide of scrf keywords, each step need read the data from chk file from the second step on. But the guide of those steps does not specify which step's chk should be used in current step. For example, the third step read the chk of first step or second step? Each step use the chk of former step? £¨ÕâÒ»¶ÎÒ²ÊÇÎÒÎʵÄÎÊÌ⣩

- Step 2: requires a copy of the checkpoint file from Step 1.
- Step 3: will work with either a copy of checkpoint file from Step 1 or from Step 2.
- Step 4: requires a copy of the checkpoint file from Step 2.
- Step 5: requires a copy of the checkpoint file from Step 4.
- Step 6: requires a copy of the checkpoint file from Step 4.
- Step 7: requires a copy of the checkpoint file from Step 6.

Please, note that there was a problem with G09 rev. A.02 because the "StateSpecific" option was connected incorrectly, but this has been fixed in our latest release, G09 rev. B.01. So, if you are using G09 rev. A.02, you would need to use "ExternalIteration" or "SelfConsistent" instead of the "StateSpecific" (shown in the example in the manual). If you are using G09 rev. B.01, then you can use "ExternalIteration", "SelfConsistent" or "StateSpecific", as the three are synonyms.

If you follow the whole example given in the manual with G09 rev. A.02 but using "ExternalIteration", you should obtain the following results on each one of the 7 proposed jobs in the example:

1) Energy of ground state optimized geometry in solution:

SCF Done:  E(RB3LYP) =  -153.851761719     A.U. after    1 cycles

2) Vertical excitation (absorption) to first excited state from Linear Response calculation in solution (using ground state optimized geometry from job 1):

Excited State   1:      Singlet-A"     4.3767 eV  283.28 nm  f=0.0000  =0.000

3) Vertical excitation (absorption) to first excited state from a non-equilibrium state-specific calculation (using "ExternalIteration" in solution (using ground state optimized geometry from job 1):

SC-PCM: The total energy including the PCM contribution is      -153.687679830 a.u.

Taking the difference of this energy minus the ground state energy (job 1), the excitation energy is 277.69 nm.

4) Geometry optimization of first excited state in solution (Final energy):

Excited State   1:      Singlet-A      3.2076 eV  386.53 nm  f=0.0014  =0.000

5) Frequency calculation to confirm that the geometry optimized in job 4 is a stationary point, and a minimum in the potential energy surface of the excited state.

6) Energy of first excited state from a equilibrium state-specific calculation (using "ExternalIteration" in solution (using optimized geometry from job 4):

SC-PCM: The total energy including the PCM contribution is      -153.707151097 a.u.

7) Energy of ground state from a non-equilibrium calculation in solution (using first excited state optimized geometry from job 4 and its reaction field from job 6):

SCF Done:  E(RB3LYP) =  -153.822029934     A.U. after   10 cycles

The difference between these last two energies gives the vertical emission energy, which, in this case, is 396.62 nm.

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