Hi Juan Pablo,

The problem with linear response methods like TDDFT is that they can sometimes give you negative excitation energies. I observed this multiple times when using ADC(2) and CC2 and the principle of getting the excitation energies in TDDFT is very similar.

I am not surprised by the outcome of your calculation. First of all, as your probably now, the equilibrium calculation means that you relax your reaction field (implicit solvent) with respect to both states and substract the energies. Since your excited state is of charge transfer character, it is much more polar than the ground state and what follows it is much more stabilized by strongly polar solvent. This may actually result in negative excitation energy. Though, it doesn't mean the result is physically correct - it is just something I would expect.

However, if you are interested in vertical excitation energies, you should not ever perform equilibrium calculation. The nonequilibrium scheme means that your implicit solvent is divided into two parts: fast part and slow part. Making things easy -slow part is supposed to mimic the positions of the solvent molecules and fast part somehow represents their polarizabilities. Since electronic excitation is practically a sub-femtosecond event, the solvent molecules have no time to redistribute, and only their polarizabilities react to the vertical excitation. Your excitation energy is significantly red-shifted, since the electric dipole moments of the ground and excited states will be most likely parallel and have the same directions. As a result the fast part is still sufficient to compensate for this modest change in the magnitude of the electric dipole moment and you get a red-shift in the spectrum.

Your red-shift in nonequilibrium solvation scheme is, however, quite significant. If this is something that you don't expect, there can be several things you can try. In reality the nonequilbirum solvation for electronic excitations is never perfect with linear response methods and it often falsifies the results. A wave function method like CASPT2/CASSCF should give you much more reliable solvatochromic shifts (you can find such a scheme in Molcas program). In this particular case your system is probably too large for CASPT2/CASSCF. In the case of TDDFT, you can perhaps have a look at some works by Benedetta Menucci - she did a lot of developments in the field. I can't give you the exact references immediately, but I remember her mentioning during a presentation, that sometimes addining some crucial explicit solvent molecules helps in obtaining more reasonable results. You can certainly find something about it in her publication record:).

Another problem can be TDDFT itself, which might have some problems in describing your system... Since you have a CT state you can try the range separated wB97XD functional (available in gaussian), and maybe your results will be a bit better.

Good luck,

Rafał

I'm not quite sure as I don't know what exactly the difference between equilibrium and non equilibrium solvation within gaussian is (by the way, how do they differ?), but I guess some explanation (unless it is a bug) could be brought by Marcus theory and respective reorganisation energy from Marcus formalism. To check that you probably can use CDFT.

Hi Juan Pablo,

The problem with linear response methods like TDDFT is that they can sometimes give you negative excitation energies. I observed this multiple times when using ADC(2) and CC2 and the principle of getting the excitation energies in TDDFT is very similar.

I am not surprised by the outcome of your calculation. First of all, as your probably now, the equilibrium calculation means that you relax your reaction field (implicit solvent) with respect to both states and substract the energies. Since your excited state is of charge transfer character, it is much more polar than the ground state and what follows it is much more stabilized by strongly polar solvent. This may actually result in negative excitation energy. Though, it doesn't mean the result is physically correct - it is just something I would expect.

However, if you are interested in vertical excitation energies, you should not ever perform equilibrium calculation. The nonequilibrium scheme means that your implicit solvent is divided into two parts: fast part and slow part. Making things easy -slow part is supposed to mimic the positions of the solvent molecules and fast part somehow represents their polarizabilities. Since electronic excitation is practically a sub-femtosecond event, the solvent molecules have no time to redistribute, and only their polarizabilities react to the vertical excitation. Your excitation energy is significantly red-shifted, since the electric dipole moments of the ground and excited states will be most likely parallel and have the same directions. As a result the fast part is still sufficient to compensate for this modest change in the magnitude of the electric dipole moment and you get a red-shift in the spectrum.

Your red-shift in nonequilibrium solvation scheme is, however, quite significant. If this is something that you don't expect, there can be several things you can try. In reality the nonequilbirum solvation for electronic excitations is never perfect with linear response methods and it often falsifies the results. A wave function method like CASPT2/CASSCF should give you much more reliable solvatochromic shifts (you can find such a scheme in Molcas program). In this particular case your system is probably too large for CASPT2/CASSCF. In the case of TDDFT, you can perhaps have a look at some works by Benedetta Menucci - she did a lot of developments in the field. I can't give you the exact references immediately, but I remember her mentioning during a presentation, that sometimes addining some crucial explicit solvent molecules helps in obtaining more reasonable results. You can certainly find something about it in her publication record:).

Another problem can be TDDFT itself, which might have some problems in describing your system... Since you have a CT state you can try the range separated wB97XD functional (available in gaussian), and maybe your results will be a bit better.

Good luck,

Rafał

Rafal, topicstarter already uses range separated functional (CAM-B3LYP). Here it worth to note, that conventional range-separated hybrids usually overestimate CT transitions energies, while usual hybrids like B3LYP underestimate.

Tricky thing here is that equilibrium solvation can stabilize CT state, hence the difference between equilibrium and non-equilibrium solvation might yield Marcus reorganisation energy, while negative excitation will be a poor approximation for electron transfer reaction Gibbs energy. To check that only explicit account for solvent is reasonable.

I know that Juan Pablo uses a range separated functional :). I noticed it. But from my experience and from what I found in the literature, wB97XD sometimes behaves better. I doesn't have to improve the results, but it might be worth trying.

In reality, I often didn't see singificant differences between B3LYP and CAM-B3LYP results even when calculating CT states. 

Rafal, check for example this DOI: 10.1039/c3cp53740d generally it is quite typical =)

Thanks for your Answers Rafal and Oleg. I cannot use a post-Hartree method because of the size of the system. Moreover, I am not using linear response but the State Specific approach within TD-DFT, which is better. I am already following the work by Menucci and Tomasi. Maybe it is just a technical issue from G09, since local excitations do look better, example:

Excitation HOMO-1 -> LUMO

gas-phase = 2.46 eV and 5.0 debye

nonequilbrium solvation = 2.42 eV and 6.4 debye

equilibrium solvation = 2.40 eV and 6.8 debye

Which is more reasonable due to this excited state is not as polar as a charge transfer states.

I am going to try your suggestion, to use wB97XD. Although I wonder also if COSMO instead of PCM would work better.

However, today I am testing with a larger cavity defined by the solvent accesible surface. It seems that larger atomic radii has a reduced effect on the energy. But I am not sure until the moment calculations are completed.

Moreover, reorganization energy of the solvent is not the same as the energy of a particular state. From the nonadiabatic scheme, initial and final states for charge transport  must be properly evaluated; then comes the solvent reorganization term.

Finally, I do need equilbrium solvation for a Franck-Condon scheme since geometry relaxation of charge transfer states is a practically impossible task for such a large system I currently study. You are right that vertical excitations are super-fast events, but I am trying to prove that a Franck-Condon equilibrated scheme may be good enough in the assessment of charge transport properties.

Many thanks for your time.

Kindest, JP

I don't think it is a technical issue. Local excitations will always look better because they have much smaller magnitude of the electric dipole moment. Ergo - they are not so affected by the solvent. Your CT state has a huge electric dipole moment (~50 Debye) and must be strongly stabilized in a polar medium. Particularly, if you relax the reaction field.

Modulating the cavity size is a very risky business... It is a very strong parameter, and of course the final effect of the solvent on the energy will be lower if you increase the atomic radii. But with such modulations you can get almost any result you like, and it's not the point...

Frankly speaking, you can't clearly say whether your negative excitation energy is an artifact of the method, technical issue (which I don't believe) or wrong starting assumption. In my opinion, if you can't afford geometry relaxation, calculating the excitation energy with equilibrium solvation will eventually lead you to some meaningless and unphysical results. The large electric dipole moment of this state says that the goemetry will be significantly reorganized in the excited state minimum (because the electronic structure is significantly reorganized). Since I do more photochemistry than photophysics and I see that such reorganization matters, I wouldn't trust such results, even if they showed something more reasonably looking.

There are some other possibilities that you can use, like Orca or Turbomole. The DFT calculation will be faster but I don't think there is nonequilbrium solvation. Perhaps you can still use the equilibrium scheme for the excited states there. 

COSMO might work better, but there are also many other potential sources of errors in such calculations. For example you use a very small basis set. Furthermore, TDDFT might have significant problems in describing your specific CT excitation ...

Pablo, to prove, that it isn't a technical issue you may try constrained DFT calculation (available in NWChem and Q-Chem for example) of CT state with same equilibrium PCM model. Advantage is that almost any hybrid functional will yield reasonable results within CDFT, whereas in TDDFT framework choice of functional seems to be crucial.

Mr. Mtz,

You cannot obtain "negative value". Furthermore, optimizing electronic transitions of push/pull systems, you should bear in mind the following important aspect, employing SMD, including equilibrium and non-equilibrium solvation approaches.

If you have focused your attention to the original description of SMD [ref. 1], there is shown that it has expressed solute-solvent interactions using model of solute "rigid". The solute-solvent boundary expressing surface interactions within the frame of solvent cavity and solvent accessible surface of solute are determined to each surface points of this boundary area.

At a given equilibrium state, thereby, the method expresses solute-solvent interactions at a fixed charge redistribution of the solute molecule. Depending of solvent polarity, however, push-pull systems have initiated charge transfer effect (attachment) accompanied with a change of geometry of molecule. Particularly the shown in the attachment example and many other ones [refs.2-6] have treated the change of the geometry of the molecule within the frame of solvents with large scale solvent polarities, T by UV-VIS, solution and solid-state IR and single crystal X-ray diffraction. The stabilization of shown aromatic and corresponding quinoide like conjugated systems is well experimentally distinguished, showing different molecular geometries and corresponding parameters, thus affecting the solvent accessible surface of solutes and charge redistribution, i.e. the electrostatic versus nonelectrostatic contributions. You have different energies to each of those forms, but those energies are taken, computing standard-state free energy of solvation by SMD approach [ref. 1]. Moreover the SMD has involved parametrization based on exerimental datasets.

Employing non-equilibrium solvation [refs.7-9] you have resonable transition as far as it takes into consideration the nuclear motions of solute, however, remains the question about initial geometry of your solute. Moreover there are not taken into consideration the specific solute-solvent interactions as well. You could pay more attention to [ref. 9], for example.

If your system has shown significant change of geometry, like this one of the example, however, you could approximate an equilibrium solvation model which cannot express the real charge redistribution, than the contribution of polarizability component in SMD should be different and that is why you have obtained an anomalous value.

If you would like to express maximum realistic system, than you should be sure are the optimized geometry realistic accounts for discussed charge redistribution and geometry.

In other words, if you would like to compute by SMD and equilibrium solvation the molecule D (attachment) in CH3CN, than you should optimized it geometry it its conjugated quinoide form. But if you would like to compute it properties in polar protic solvents like H2O or CH3OH that you should optimized your initial state taking it aromatic form/s F or C. To illustrate these differences there are optimized forms A and C (attachment). The energies and solvent accessible surfaces are shown as well. Nevertheless that there have predicted different exitations comparing to the experimental data, the values are "positive", not "negative" ones.

You could pay attention, also, to our theoretical and experimental data about sets of push/pull dyes treating their tautomerizm and aggregates [refs. 2-6].

If you have performed multi-steps computation, are you sure that the links between different steps are properly given?

[1] A. Marenich, C. Cramer, D. Truhlar, Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions, J. Phys. Chem. B 2009, 113, 6378-6396

[2] Kolev, T.; Koleva, B.; Stoyanov, S.; Spiteller, M.; Petkov, I. (2008) The aggregation of the merocyanine dyes, depending of the type of the counterions, Spectrochimica Acta A 70, 1087-1096

[3] Kolev, T.; Koleva, B.; Spiteller, M.; Mayer-Figge, H.; Sheldrick, W. (2008) The crystal structure and optical properties of 1-methyl-4-[2-(4-hydroxyphenyl)ethenyl]pyridinium dihydrogenphosphate: New aspects on crystallographic disorder and its effect on polarized solid-state IR spectra, Dyes and Pigments 79, 7-13

[4] Ivanova, B.; Nikolova, R.; Lamshöft, M.; Tsanova, P.; Petkov, I.; Ivanov, P.; Spiteller, M. (2010) Surface interaction and self-assembly of cyclodextrins with organic dyes, J. Inclus. Phenom. 67, 317-324

[5] Lamshöft, M.; C. Stolle, J. Storp, B. Ivanova, M. Spiteller (2012) Structural and spectroscopic study of novel Ag(I) metal-organic complexes with dyes-experimental vs. theoretical methods Inorg. Chim. Acta, 382, 96-104

[6] Ivanova B., Spiteller M. (2013) Optical and nonlinear optical properties of new Schiff's bases - experimental vs. theoretical study of inclusion interactions" J. Inclus. Phenom. 75, 211-221

[7] R. Cammi, J. Tomasi, Nonequilibrium Solvation Theory for the Polarizable Continuum Model: A New Formulation at the SCF Level with Application to the Case of the Frequency-Dependent Linear Electric Response Function, Int. J. Quant. Chem. 29, 465-474 (1 995)

[8] R. Bianco, J. Timoneda, J. Hynes, Equilibrium and Nonequilibrium Solvation and Solute Electronic Structure. J. Phys. Chem., 98, 1994, 12103-12107

[9] S. Tucker, D. Truhlar, Effect of Nonequilibrium Solvation on Chemical Reaction Rates. Variational Transition-State-Theory Studies of the Microsolvated Reaction Cl-(H2O)n+CH3Cl, J. Am. Chem. Soc., 112, 1990, 3347-3361.

https://www.researchgate.net/post/How_to_perform_Corrected_Linear-Response_PCM_claculation_with_Gaussian_program

https://www.researchgate.net/post/How_to_perform_the_PCM_corrections_to_get_absorption_and_emission_energies

http://gaussian.com/scrf/

http://www.uwyo.edu/kubelka-chem/mm_notes_17.pdf

Article DFT and TD-DFT study on the optical and electronic propertie...

Hi Pablo. I explained this in a paper on JCTC in 2015 together with B. Mennucci, D. Jacquemin and C. Adamo. The reference is J. Chem. Theory Comput. 2015, 11, 5782−5790.

The reason is that in the External Iteration the iterations are performed on the total excited state density (P i = P 0 + P Δ 0i ) and therefore the ground state contribution is also recalculated by iterating the KS-DFT equation in the presence of solvent charges calculated for the excited state. The GS of reference for the ES is no more variational in this manner.

Use a corrected linear response calculation or VEM.

Here the tutorial:

https://molecolab.dcci.unipi.it/tools/white-papers/pisalr/

Article Electronic Excitations in Solution: The Interplay between St...