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Using Density Based Indexes and Wavefunction Methods for the Description of Excited States: Excited State Proton Transfer Reactions as Test Case Juan Sanz García, Federica Maschietto, Marco Campetella, and Ilaria Ciofini J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b10033 • Publication Date (Web): 12 Dec 2017 Downloaded from http://pubs.acs.org on December 22, 2017

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The Journal of Physical Chemistry

Using Density Based Indexes and Wavefunction Methods for the Description of Excited States: Excited State Proton Transfer Reactions as Test Case Juan Sanz García,a,* Federica Maschietto a, Marco Campetella a, Ilaria Ciofini a,* a

Chimie ParisTech, PSL Research University, CNRS, Institut de Recherche de Chimie Paris, F-75005 Paris, France

ABSTRACT To provide tools to interpret photochemical reactions, in this paper we demonstrate how a recently developed density-based index (DCT), up to now used in conjunction with Time Dependent Density Functional Theory methods, can be extended to multiconfigurational methods. This index can guide chemists in the interpretation of photochemical reactions providing a measure of the spatial extent of a photo-induced charge transfer and, more generally, of charge transfer phenomena. This qualitative and quantitative description can be particularly relevant in the case of multi-configurational calculations providing a simple tool for the interpretation of their complex outputs. To proof the potentiality of this approach we have considered a simple intramolecular excited state proton transfer reaction as study case and applied both wave-function (CASSCF-CASPT2) and density-based methods in conjunction with a DCT analysis. Our results confirm that, also in the case of multiconfigurational methods, the DCT provides very useful information about the structural reorganisation of a molecule at the excited state.

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1. INTRODUCTION Recently there has been an increasing interest in the use of theoretical approaches for the description of excited state (ES) phenomena correlated to the plethora of their experimental applications of technological relevance.1–5 Both methods rooted on density functional theory (DFT) and wavefunction approaches (post-Hartree-Fock (HF) methods) were indeed extensively used both to characterize the absorption/emission properties of systems6–10 or to study the excited state potential energy surface (PES) to get insights on their reactivity,11–15 even in complex environments.16–19 Furthermore, more recently, many descriptors have been developed and used essentially in conjunction with time dependent DFT methods (TD-DFT) both as diagnostic indexes for the methods reliability20–22 and for describing the nature of the electronic excited state under analysis.23–31 Not surprisingly, excited state proton transfer reactions (ESPT) and, more particularly, intramolecular ESPT (ESIPT) have been often considered to benchmark and assess the quality of the underlying theoretical methods in the description of excited state profiles due to the intrinsically well-defined reaction coordinate28 and to the extremely flat potential energy surface which makes the description of the excited state a challenging task for theoretical approaches.27 Indeed, this type of systems are characterized by a proton transfer which occurs at the excited state between neighbouring donor-acceptor atoms (such as oxygen or nitrogen).32–36

Figure 1. Schematic representation of the ESIPT reaction.


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For large number of systems involved in ESIPT and showing oxygen and nitrogen as heteroatoms the ground state present an energetically favourable enol form (-OH, E, Figure 1). This tautomer may exhibit a strong intramolecular hydrogen bond with the acceptor atom (a nitrogen atom in the case depicted in Figure 1). As a result of a photon absorption, the acidity of the enol group is increased so that the keto conformer (K* in Figure 1) becomes the most stable form at the excited state. Hence, a light induced tautomeric reaction occurs giving rise to the four level diagram depicted in Figure 1. If the E* and the K* species are stable enough, they can both radiatively decay into the corresponding ground state forms and the molecule may display two distinct emission bands in the corresponding electronic spectra.

This

intriguing dual-emission phenomenon has been used in designing novel chemosensors in various target applications.24–29,32,33 In literature, probably two of the most experimentally studied ESIPT dyes are represented by the 2-(2hydroxyphenyl)benzothiazole (HBT) and 2-(2- hydroxyphenyl)benzoxazole (HBO) molecules37,38 schematically depicted in Figure 2.

Figure 2. Prototype molecules which can undergo ESIPT.

Here we will use the HBT molecule and a simplified model of it (2-(2hydroxyphenyl)thiazole HT, in Figure 2) as prototype systems to analyze the effect of the use of wavefunction methods or TD-DFT approaches in the description of the ES potential energy surface. More in details, first we will assess, at TD-DFT level, the relevance of the reduced model (HT) for representing the ground and excited state properties of the full HBT molecule, both in terms of energetic and of charge transfer (CT) character27 -here measured by the use of a recently developed density based index (DCT)20-. Next, the excited state potential energy surface and 3 ACS Paragon Plus Environment


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the electronic properties of the HT molecule will be analyzed both at TD-DFT and at CASSCF/CASPT2 level. The latter calculation become achievable thanks to the reduced dimension of the molecule reflected in a more affordable active space which is reduced from 18 electrons in 16 orbitals (18e,16o) for the HBT molecule to 14 electrons in 12 orbitals (14e,12o) for the HT molecule. These post-HF calculations will be compared to the TD-DFT ones to analyze the impact of the methods on the excited state potential energy surface both in terms of energy and of CT character. Noteworthy, for the first time, the DCT evaluation is here obtained by means of a multi-configurational theory.

Indeed, up to now, to the best of our knowledge the

computation of density-based indexes such as DCT has been limited to DFT-based and CIS approaches. A specific aim of this work will therefore be to assess if the relation between the energetic features of the reaction and the values of the DCT indexes previously defined for TDDFT methods also holds in the case of a CASSCF-CASPT2approach further validating their use. This work is structured as follows: after the computational protocol (Section 2), results obtained at TD-DFT level for the HBT molecule and the HT model are reported in Section 3.1. Next, in Section 3.2 the energetic (ES-PES) and the CT character (DCT index) computed for the HT model at TD-DFT and post-HF level will be compared by scanning the PES along the two –most relevant- reaction coordinates. Finally, some general conclusions are reported. 2. COMPUTATIONAL DETAILS Ground State potential energy surfaces (PES) of HBT and HT molecules have been evaluated performing a two-dimensional (2D) relaxed scan. A 2D grid has been generated optimizing one hundred homogeneously distributed structures with two constrained degrees of freedom: the N–O and O–H distances. In particular, the structures were generated varying the N–O distance from 2.54 Å to 2.72 Å in increments of 0.02 Å, and the O–H distance from 0.99 Å to 1.89 Å in increments of 0.10 Å in order to encompass both the enol and the keto optimized forms. On the same grid the DCT index is computed. For comparison purposes, the GS relaxed scan was performed at Hartree-Fock, Density Functional Theory (DFT) and Complete Active Space Self Consistent Field (CASSCF)39 levels, as analytical gradients are available for all these methods. For the excited state properties, Configuration Interaction Singles (CIS),40 TDDFT41 and Complete Active Space with Second-order Perturbation Theory (CASPT2)42 calculations, respectively, were vertically performed on this grid. For the DFT and TD-DFT calculations, two different functionals were used: i) a global hybrid functional (PBE043) and, 4 ACS Paragon Plus Environment

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ii) a range separated (asymptotically correct)44 (LC-PBE45,46).

The same computational

protocol was also used to perform a relaxed scan of the ES at CIS and TD-DFT level. The Wave Function (WF) used in the CASPT2 calculations was computed using the StateAverage-CASSCF (SA-CASSCF) technique with four equally weighted roots (the ground state and three more excited states) and an active space consisting on 14 electrons in 12 π orbitals delocalized in the whole planar HT molecule. Although CASSCF calculations are not able to recover dynamic correlation unless the active space is prohibitively large, CASSCF optimizations were the only feasible alternative to compute the optimized geometry grid. Evaluation of all optimized geometry energies at the GS (and ES) as well as vertical excitation energies in the Franck-Condon (FC) region were performed at the 4SACASSCF(14,12)/CASPT2 level of theory. The imaginary shift technique (0.2 a.u.) was employed to avoid the possible presence of intruder states,47 as previously reported in the literature for a similar organic chromophore as described in ref. 36. All calculations, were carried out using the same diffuse-augmented polarization valence-double-ζ basis set (6-31+G(d))48 with one set of d polarization functions49,50 and a set of s and p diffuse functions51,52 for all atoms but hydrogens. All calculations, but the post-HFbased ones, were performed with the Gaussian 16 quantum package.53 CASSCF as well as CASPT2 calculations were performed using the MOLCAS 8.0 quantum package.54 All calculations have been performed in the gas phase. As it has been shown in previous studies,24–27 the DCT density-based index allows in a simple and intuitive way to quantify the spatial extent of a charge transfer excitation. Using the electronic densities of the ground and excited state of interest (here the first singlet), ρGS(r) and ρEX(r), respectively, the DCT has been mapped on the optimized GS and ES grids. In order to briefly remind the construction of the DCT index, one need to: i) define the electronic density variation between ground and excited state upon excitation: ∆ρ (r ) = ρEX (r ) − ρ GS (r )

(1)

ii) define two different functions which describe the spatial regions within a molecule where the density has increased (ρ+(r)) or decreased (ρ-(r)) upon excitation:



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∆ρ (r ) if ∆ρ (r ) > 0 if ∆ρ (r ) < 0  0

(2)

∆ρ (r ) if ∆ρ (r ) < 0 if ∆ρ (r ) > 0  0

(3)

ρ + (r ) = 

ρ − (r ) = 

iii) define the barycenters associated to these density distributions regions:

R+ =

∫ rρ (r )dr = (x ∫ ρ (r )dr

+ , y + , z+ )

(4)

∫ rρ (r )dr = (x ∫ ρ (r )dr

− , y − , z− )

(5)

+

+

R− =

−

−

iv) and finally, compute the distance between these barycenters: DCT = R+ − R−

(6)

For TD-DFT calculations, the DCT index was directly computed using the Gaussian 16 program, using therefore unrelaxed densities. For the CASPT2 calculations the generation of two different files containing the ground and excited state densities on a grid of points around the molecule was necessary, for each of the structure analyzed. The DCT values, corresponding to relaxed densities, were next computed using an in-house developed software.55 In a recent study the equivalent use of relaxed and unrelaxed density in the case of excitation with limited CT character has been demonstrated thus validating our approach.55–57 3. RESULTS AND DISCUSSION 3.1 Assessment of the Model System : HT vs HBT In order to validate the use of the HT system (Figure 1) as a reasonable model to describe the ESIPT reaction of HBT, TD-DFT calculations were performed using different functionals for both systems. Energy and DCT maps were computed for both systems, as described in Section 2. In particular, ground state PESs were constructed, for both HT and HBT, performing a 6 ACS Paragon Plus Environment

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relaxed scan along the N−O and O−H coordinates, computed at the PBE0 level of theory, followed by single point TD-DFT calculations performed using the PBE0 and LC-PBE functional as well as at CIS level. Excited state parameters were obtained vertically from the optimized ground state geometries, using the same approach. It is worth mentioning that CIS results are included here only for completeness and are not intended to represent the standard for post-HF calculations that will be discussed only later in the case of the HT molecule. All geometries obtained show a planar structure. The energetic parameters most relevant to describe the enol to keto tautomerization, as extracted from the computed 2D maps, are reported in Table 1. At the GS, both for the HT and HBT molecule (HBT values will be reported in parentheses in the following) the minimum energy tautomer is the enol one, the keto form being computed higher in energy independently of the method considered. Though the keto-enol energy difference is dependent of the method used, for a given approach the difference in relative stability of the two forms is practically equivalent when considering the HT or the HBT form. In particular, at PBE0 level the keto tautomer is computed 47.7 kJ/mol (43.1 kJ/mol HBT) higher in energy than the enol one, while the energy gap predicted at LC-PBE0 level is 54.2 kJ/mol (52.2 kJ/mol HBT), and at HF level is 57.8 kJ/mol (52.8 kJ/mol HBT). Therefore for GS minima, HT seems to be a good model for HBT. The same holds when considering the PT reaction barrier computed at the GS. Indeed, at the PBE0 level the estimated GS activation energy (Table 1) for enol-keto tautomerization of HT is about 52.2 kJ/mol and 50.1 kJ/mol for HBT. The reverse reaction show a barrier of ca. 4.5 kJ/mol for HT and of 7.0 kJ/mol HBT, thus validating the use of the HT model. The same type of conclusions can be drawn analyzing the results obtained at LC-PBE level and CIS (independently from the intrinsic overestimation of the energy barrier). At LC-PBE for instance, though the computed barriers are higher than those computed at PBE0 level, very similar values are obtained for the HT or HBT molecules that are ca. 58.2 and 4.0 kJ/mol for the forward and reverse tautomerization for HT to be compared with 55.4 and 3.2 kJ/mol for HBT. HT//HBT

HT//HBT

HT//HBT

PBE0

LC-PBE

HF/CIS

∆(Keto-Enol)GS

47.7// 43.1

54.2 //52.2

57.8// 52.8

∆(TS-Enol)GS

52.2//50.5

58.2//55.4

91.0//88.7

-24.8//-24.2

-33.0//-35.0

-25.1//-26.7

∆(Keto-Enol)ES



∆(TS-Enol)ES

1.6// 4.2

3.5//4.2

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38.9//44.4

Table 1: Estimated relative stability and reaction barrier for keto-enol tautomerization of HT and HBT, (in kJ/mol). All values are calculated with respect to the enol form on a 2D grid of structure optimized at the GS at PBE0 level (see text for details).

In conclusion for the ground state energetics (both relative stability of the minima and barrier) the HT molecule seems to quantitatively reproduce the features of the HBT one independently of the DFT method chosen with discrepancies always lower than 4 kJ/mol. The same conclusion can be drawn by analysing the energetic profile of the S1 potential energy surface computed at different TD-DFT level. Indeed, though in this case all methods predict a more stable keto form and much lower reaction barrier (in agreement with the experimentally observed ESIPT phenomena), HT and HBT results are quantitatively comparable thus further confirming the suitability of HT as model for the energetic profile of the PT both at the ground and the excited state. Analysis of the S1 PES surfaces, reported in SI (see Figures S1– S8 for HBT and Figures S9 – S16 for HT) allows showing that the global profiles are also qualitatively equivalent. Indeed both in the case of HT and HBT, the PT occurs through a synchronous contraction of the N−O distance and an elongation of the O−H one, in accordance with previous results27,35 Following the minimum energy pathway computed for HT and HBT on the S1 PES allows to identify three consecutive phases: first the distance N−O decreases (around 2.54 Å); next, the TS is reached (corresponding to a minimal N−O distance) and finally the proton is transferred. At the transition state the N−H bond measures about 1.20 Å (for both HT and HBT), while the O−H bond is stretched by ca. 0.60 Å as compared to the original enol structure. To further analyse if HT can be used to simulate the behaviour of HBT, besides the energy profiles, we decided to compare also the electronic rearrangement of the molecule upon excitation on the same 2D map. To this end, DCT values were computed for each grid point and plotted as 2D maps. In agreement with previous studies of DCT evolution along ESIPT reactions,27 and independently of the method used, for both HT and HBT as the proton is transferred from the oxygen to the nitrogen atom, the DCT index increases up to a maximum value before decaying to a lower value, once the keto form is formed. The transition state lies at the point of the reaction path where the effective charge transfer distance (i.e. the DCT) is the largest. The final decrease of the DCT is conditional to post PT geometrical rearrangements. In the present case, the keto form does not relax significantly and, accordingly, no major changes in the DCT value are computed.


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The DCT values computed for the keto and enol forms both at the ground and the excited state at different levels of theory are reported in Table 2.

HT//HBT HT//HBT HT//HBT PBE0

LC-PBE

CIS

DCT

1.44//1.40

0.82//0.78

0.39//0.30

Keto DCT

0.98//1.14

0.34//0.25

0.44//0.44

Enol

Table 2: Computed DCT values (Å) corresponding to enol and keto form of the HT. Values correspond to the minima computed on a 2D grid of structures optimized at the GS at PBE0 level (see text for details).

Clearly, the use of the HT model is justified since the results obtained are quantitatively equivalent to those of HBT (Table 2). These results indeed clearly show that the CT character and thus the nature of the electronic transition is the same for both systems. Up to now, we have used PBE0 ground state optimized geometries to construct the GS and ES 2D maps. For the sake of completeness and in order to check that no artefact was introduced in such way, optimized ground state and corresponding vertical excited state surfaces were also computed at each level of theory. Since all different methods result in nearly identical geometries, no significant change was found in the two-dimensional contour maps (all corresponding data are reported in Supporting Information Tables S1-S7 for HT and Table S12-S16 for HBT). Therefore, independently of the level of theory used, the results obtained for HT and HBT both on energetics and on the nature of the excited state fully validate the use of HT as model system to elucidate quantitatively ESPT phenomena occurring in the HBT molecule. Thus, in the following we will focus only on the HT model to extendthis study to multi-reference postHF methods. 3.2 Description of the ESIPT in HT Using CASSCF-CASPT2 Calculations and Density Based Indexes As previous studies based on DFT and TD-DFT calculations showed, ESPT reactions can be mapped and described using Density Based indexes that can help in locating minima and transition states on excited state potential energy surfaces.25–28 In order to validate this analysis and extend it to CASSCF-CASPT2 methods, the HT molecule (that we demonstrate as a suitable model for the real HBT system) will be analysed at CASPT2 level taking care of establishing the link between the computed PES and the density based index, DCT. Before analysing in detail the computed data, it is important to remind that neither the ground and 9 ACS Paragon Plus Environment


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first excited state PESs nor the first and second excited state surfaces of HT cross each other when the molecule is kept planar (as in the present grid) so that our approach focusing on one –isolated- excited state for the calculation of the DCT keeps its validity. It is also worth noticing that within the PES region studied, that is as long as the molecule keeps planar the electronic nature of the first singlet excited state do not change

(π- π* state) with no

interseaction with a n- π* state, which can be indeed be stabilized upon deplanarization of the molecule. Let us first illustrate the topology of the ES PES and the corresponding DCT map computed at CASPT2 level focusing on the Franck Condon region. Based on CASPT2 calculations and in agreement with DFT results, at the ground state, the HT molecule should be exclusively in the enol tautomer form due to its very large stability with respect to the keto form (60.9 kJ/mol, Table 3). After the absorption of a photon, the redistribution of electronic density across the molecule increases the acidity of the oxygen and the basicity of the nitrogen. This results in the fast tautomerization process in the excited state. In an ideal donoracceptor model, the initial absorption may be described as a CT between the oxygen and the nitrogen atoms; however this process actually involves both the phenol to the thiazol moieties as confirmed by the difference between of the sums of CASPT2 Mulliken charges for the phenol moiety at the ground (0.31 |e-|) and excited state (0.44 |e-|) and the same for the thiazol moiety at the ground (-0.31 |e-|) and excited state (-0.44 |e-|). Nonetheless, due to the arbitrary nature of the partition scheme used to compute atomic charges, the evaluation of the CT phenomena is very difficult to be assessed using only a charge analysis, the use of different charge partition schemes eventually providing both quantitatively and qualitatively different results.58 The use of an arbitrary partition to define atomic charges can be avoided applying a DCT based analysis which provides a neat solution to this ambiguity. This index allows not only to quantify the spatial extent of the CT excitation, but also allows one to better define the donor/acceptor molecular regions as computed from multi-reference calculations, therefore helping both in a quantitative and qualitative assessment of the charge transfer phenomenon. This information is indeed inherently provided by the position of the positive and negative barycentres of charges (also required to compute the DCT itself). CASPT2

CASPT2

∆(Keto-Enol)GS

60.9

DCT

∆(TS-Enol)GS

60.9a

Enol

--b

DCT

∆(Keto-Enol)ES

1.01


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∆(TS-Enol)ES

--

Keto

0.18

Table 3: Estimated relative stability and reaction barrier for keto-enol tautomerization of HT (in kJ/mol) at the CASPT2 level of theory. All values are calculated with respect to the Enol form on a 2D grid of structure optimized at the GS at PBE0 level (left). Computed DCT values (Å) corresponding to enol and keto form of HBT and HT. Values correspond to the minima computed on a 2D grid of structure optimized at the GS at PBE0 level a b (right) (see text for details). No transition state found in the ground state PES. No E* minimum found in the excited state S1 PES.

As it can be observed in Figure 3, at the ground state enol minimum, the initial photoinduced electronic rearrangement may be described as a ‘partial’ intramolecular CT as evidenced by the small computed DCT value (1.04 Å) corresponding to a transition from the phenol moiety to the C1−C2 bond. Of note this value is smaller than what computed at TD-DFT level. As the reaction progresses through the vertical S1 PES from point a) to point b) (Figure 4), the molecule experiences a skeletal contraction, reducing by 0.1 Å the N−O distance (and consistently incrementing the O−H bond distance by 0.1 Å), which results in an increment of 0.21 Å in the DCT. From point b) to point c) an increase of 0.2 Å in the O−H bond distance will result in a doubling of the increment of the DCT. In the last step (from point c) to point d)) corresponding to a 0.4 Å increment of the O−H bond distance, the K* tautomer is formed and the DCT decreases to its lowest value. Indeed, the geometry corresponding to the minimum in the ‘DCT surface’ is very close to the minimum in the S1 PES, as it will be discussed in the following subsections.

Figure 3: DCT character following the steepest-decent pathway through the vertical S1 PES from a) to d) (see Figure 4). Blue dot DCT positive barycentre, R+, red dot DCT negative barycentre, R-. DCT values a) 1.04 Å ; b) 1.25 Å ; c) 1.62 Å ; d) 0.42 Å.

Interestingly, contrary to the PBE0, LC-PBE and CIS vertical S1 PES, the CASPT2 one does not show any E* minima, but only a steep downhill slope at the Franck-Condon region which 11 ACS Paragon Plus Environment


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points towards the global K* minima with no other local minima throughout the steepest decent trajectory. This barrierless adiabatic S1 pathway is not surprising and in agreement with previous findings27 on ESIPT reactions studied at CASSCF/CASPT2 level.

Figure 4: The ‘Vertical’ S1 LC-PBE Energy in the top left, the ‘Vertical’ LC-PBE DCT in the bottom left, the ‘Vertical’ S1 CASSCF/CASPT2 Energy in the top right and the ‘Vertical’ CASSCF/CASPT2 DCT in the bottom right corner. All geometries have been computed at the ground state PBE0/6-31+G* level of theory. White arrow: ESIPT straight line pathway, dashed arrow: ESIPT minimum energy pathway, dashed black line : steepest decent pathway from Franck-Condon region to the ‘minimum’ enol* tautomer.

It is very interesting to notice that a direct comparison of the topological features between S1 PES and DCT surface reveals remarkable common patterns in both surfaces (Figures 4 and S9 – S18 in the Supporting Information) independently of the method used. For instance, in the case of LC-PBE (see top of Figure 4) and PBE0 functionals (see Supporting Information Figure S3) both surfaces present a very flat E* minimum, while a steep well defined minimum appears in the K* region. It is also important to highlight the presence of a maxima region going from the E* to K* forms which appears in both surfaces (S1 PES and DCT). In the case of the CIS method both surfaces are remarkably similar as well, presenting the same features as in the case of the DFT surfaces, except for the fact that the E* minimum is, in the CIS case, much steeper both in the S1 PES and in the DCT surface (see Supporting Information Figure S1). Finally, in the case of the CASPT2 calculations no E* 12 ACS Paragon Plus Environment

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minimum is found in the S1 PES, while the K* minimum is located in the very same region in both surfaces (see right side of Figure 4). As mentioned in the previous section, optimizing the GS geometries at different levels of theory affords relatively identical structures. This results in S1 PES and DCT surfaces being qualitatively the same with no remarkable differences to those computed using the PBE0 ground state optimized grid. On the other hand, the effect of using different structures can be analysed by optimizing the geometries at the excited state S1. These latter are reasonably different from those obtained for the GS. When computing the 2D grid values using these optimized S1 structures, it can be observed as a general trend that the minima in the excited state PES become steeper and well-defined, compared to those observed in the vertical 2D grids obtained using the GS geometries. Besides, what it is even more remarkable is the fact that the corresponding DCT surface behaves in a very similar way, accentuating the minima regions, and thus recovering the information of the molecular energetic changes. Being qualitatively extremely similar to the ones reported in Figure 4, these maps are reported in Supporting Information (Figures S12 – S18). 4. CONCLUSIONS Using a prototype excited state reaction, namely an excited state proton transfer reaction as test case we demonstrated that density based descriptors (such as the DCT index) can be safely used to not only to qualitatively describe but also to quantitatively analyse excited state evolution both at TD-DFT level but also at multi-reference post-HF level (here CASSCFCASPT2). In the latter case, the use of density based indexes may be of particular relevance : -

To provide a qualitative description of the excited state

-

To quantify CT in complex systems avoiding arbitrary evaluation based on charge partitioning

Of course all limitations concerning the DCT itself (for instance its null value by construction in the case of systems with quadrupole-like symmetry) hold independently of the underlying electronic method used to access to ground and excited state densities. Nonetheless, our results confirm that all relations previously derived at TD-DFT between excited state potential energy surfaces and DCT evolutions are still valid when using CASSCFCASPT2approaches, thus confirming the use of the DCT index as general tool for the description of excited state reactivity involving ES with sizable CT character.



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ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: 2D Excited State S1 PES and related DCT computed for HBT and HT at various levels of theory. AUTHOR INFORMATION Corresponding Authors *J. Sanz García. E-mail: [email protected] *I. Ciofini. E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 648558 STRIGES CoG grant).


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Using Density Based Indexes and Wave Function Methods for the

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