Intramolecular Charge Transfer and Local Excitation in Organic

Subscriber access provided by Kaohsiung Medical University

C: Physical Processes in Nanomaterials and Nanostructures

Intramolecular Charge Transfer and Local Excitation in Organic Fluorescent Photoredox Catalysts Explained by RASCI-PDFT Davide Presti, Donald G. Truhlar, and Laura Gagliardi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01844 • Publication Date (Web): 14 May 2018 Downloaded from http://pubs.acs.org on May 15, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Prepared for J. Phys. Chem. C – May 11, 2018

Intramolecular Charge Transfer and Local Excitation in Organic Fluorescent Photoredox Catalysts Explained by RASCI-PDFT Davide Presti, Donald G. Truhlar* and Laura Gagliardi* Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-043, USA.

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 35

2 Abstract We investigate the electronically excited states of two recently synthesized organic fluorescent photoredox catalysts of the dihydrophenazine family. The mixed charge transfer and local excitation behavior of dark and bright transitions is unveiled by multi-configuration pair-density functional theory (MCPDFT) based on a restricted active space configuration interaction (RASCI) wave function (RASCIPDFT). The RASCI-PDFT calculations give an accurate description of the experimental optical absorption spectra with active spaces too large for conventional complete active space SCF (CASSCF) calculations. These results were achieved by the inclusion of many valence orbitals in the active space and their optimization within a cost-effective RASSCF framework without a RAS2 subspace, followed by calculations at the RASCI level including orbitals in RAS2. This novel strategy can be extended to systems that need a large number of orbitals in the active space.


Page 3 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3

1. Introduction Luminescent materials find a vast range of applications. A few examples are LEDs (light emitting diodes)1 and OLEDs (organic LEDs),2,3 light and gas sensors,4–6 lasers,1,7,8 solar cells,9–11 and photocatalysts.12–14 The optical behavior of these materials is often complex and hard to understand at the atomistic scale. For example, the excited state may differ from the ground state by charge transfer,15,16 tautomerism, or large internal rotation or displacement of functional groups.17 The combination of these effects16–18 sometimes renders experimental observations challenging to interpret, even more when going from the study of isolated gas-phase molecules to condensed phases where collective and environmental effects arise.19,20 In the present work, we study the nature of excited states of organic fluorescent photoredox catalysts (PCs) with emphasis on the competition between intramolecular π-π* charge-transfer (CT) and local excitations (LE). Dihydrophenazine derivatives have recently been recognized21,22 as efficient PCs for the organocatalyzed atom transfer radical polymerization (O-ATRP) of methylmethacrylate. ATRP is an increasingly popular methodology23 because it can yield high conversion with small dispersity of molecular weight in the product polymer. Beyond the catalytic efficiency that plays a key role in large-scale industrial applications, O-ATRP with dihydrophenazines has advantages from the point of view of green chemistry because the catalysts are metal-free, fully organic catalysts that do not release unsafe by-products, and they are activated by natural light. The photocatalytic process for methylmethacrylate polymerization is postulated to involve electron transfer from a CT state (S1 or T1) to produce the doublet radical cation (2PC·+) and the ion-pair species 2

PC·+Br–. It has been inferred, based on a combination of experiment and quantum mechanical calcula-

tions, that charge separation in the excited states, in particular, the presence of excited states with one singly-occupied molecular orbital (SOMO) localized on the dihydrophenazine ring system and the other



Page 4 of 35

4 localized on an aryl substituent, slows down fluorescence and thereby facilitates the electron transfer of the reductive step in the polymerization mechanism; this provided an explanation of why naphthylsubstituted dihydrophenazines are good O-ATRP photocatlysts.21,22,24 Low-lying CT states and good catalytic activity were predicted21,22,24 for the isomers 5,10-di(1-naphthyl)-5,10-dihydrophenazine (1DINAPH) and 5,10-di(2-naphthyl)-5,10-dihydrophenazine (2-DINAPH), which are shown in Figure 1a.

Figure 1. a) 2D and 3D structural representation of (top) 1-DINAPH and (bottom) 2-DINAPH. The 3D structures were optimized by CAM-B3LYP calculations in the gas phase. b) Jablonski diagram showing radiative and non-radiative processes (the latter in violet), inspired to Figure 3 of Ref.22 IC: internal conversion; ISC: intersystem crossing. Low-probability radiative processes are depicted with dashed lines.

Charge transfer states are expected to be dark in absorption, and the bright singlet-singlet excitations are expected to be higher in energy than the charge transfer excitations (see Figure 1b). After internal conversion to S1, the fluorescence is red shifted, but in polar solvents 1-DINAPH and 2-DINAPH have


Page 5 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5 much larger red shifts than phenyl-substituted dihydrophenazines, and these solvatochromic shifts were interpreted as further evidence for large CT character in the naphthyl-substituted compounds.22 The goal of the present study is to better understand the excited states of 1-DINAPH and 2-DINAPH. We first attempt to describe the UV–visible absorption spectral and energetic properties of the two compounds, both in gas phase and in solution, using linear-response Kohn-Sham time-dependent density functional theory (LR-KS-TDDFT), but the presence of CT transitions is often problematic for LR-KSTDDFT.25–27 Therefore we next turn to a technique, multi-configuration pair-density functional theory (MC-PDFT),28–30 better able to deal with strongly multiconfigurational states, in particular we use PDFT calculations based on complete-active-space self-consistent-field (CASSCF31) wave functions, restricted active space self-consistent field (RASSCF)32 wave functions, and restricted active space configuration interaction (RASCI33) wave functions. The final results of the present paper are generated by calculating the PDFT or PT2 energy from a RASCI wave function (i.e., RASCI-PDFT). The RASCI wave functions are generated by using orbitals optimized in a RASSCF calculation without a RAS2 active subspace. This SCF step is followed by a RASCI calculation in which the orbitals are not reoptimized; as compared to the earlier RASSCF step, the RASCI step has a smaller number of orbitals in the active space, but it includes some orbitals in RAS2. Then, the final energies are calculated by either PT234 (2nd order perturbation theory) or PDFT (pair-density functional theory) based in either case on the RASCI wave function (rather than the RASSCF wave function) as the reference wave function. While RASCI calculations following RASSCF calculations have been performed in the past,34–36 and large active spaces employed via either the density matrix renormalization group approach – DMRG-CASSCF37,38/CASSCI39 – or combined with full configuration interaction quantum monte carlo (FCIQMC-CASSCF),40 the introduction of the RASCI



Page 6 of 35

6 step between the RASSCF step and the PDFT one is new, and we will show that it can be a powerful method for treating large and complex systems.

2. Computational Methods 2.1 KS-DFT and LR-KS-TDDFT For 1-DINAPH, density functional approximations (DFAs) of various types have been employed, both local and hybrid, where hybrid functionals include a percentage X of Hartree–Fock nonlocal exchange. In particular we used PBE41 (local gradient approximation), PBE042 (global hybrid gradient approximation with X = 25), CAM-B3LYP26 (range separated hybrid gradient approximation with X = 67 at large inter-electronic separation), M1143 (range-separate hybrid meta approximation with X = 100 at large inter-electronic separation), and ωB97X44 (range-separated hybrid gradient approximation with X = 100 at large inter-electronic separation). The range-separated functionals were chosen because this kind of functional has better performance for charge-transfer (CT) excitations – for which selfinteraction errors can dominate, especially at long-range25,45 – and can give a better description, with respect to standard DFAs, of transitions involving small overlaps between molecular orbitals.46 Moreover, M11 is also reasonably accurate for noncovalent interactions.47 The 6-31+G(d,p) basis-set48,49 is employed for all KS-DFT and LR-KS-TDDFT calculations. (See Table S3 of Supporting Information – SI – for comparison of structural parameters calculated with this and a larger basis-set50). Geometry optimizations were carried out both in the gas phase and in DMF (N,N-dimethylformamide) solvent, which was included implicitly51 by the polarizable continuum model52,53 in the integral equation formalism of the polarized continuum model (IEFPCM)52,53 with UFF radii54 scaled by 1.1. Optimized


Page 7 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


7 geometries for the closed-shell singlet ground-state are reported in the Supporting Information of Ref.21 and were taken as starting structures to be used as input for the present ground-state optimizations. Frequency calculations were performed for optimized structures to ensure that they are local minima on the potential energy surface (PES). Several DFAs were compared for vertical excitation energies of 1-DINAPH. The computed energy of the lowest eight excited singlets were compared (see SI, Table S4) with the value (3.43 eV) corresponding to the experimental λmax (362 nm) of the UV-Visible absorption spectrum in DMF solvent, reported in Figure S9 of Ref. 21. On the basis of this comparison we chose CAM-B3LYP for further calculations on both 1-DINAPH and 2-DINAPH (see Tables S1-S4, Figures S1-S2, and discussion on page S-11 of Supporting Information). [Similar experimental and theoretical results were obtained in dimethylacetamide (DMA) solvent by Lim et al.22 (DMA and DMF have similar dielectric constants, 37.781 and 37.219, respectively.)] Vertical excitation energies were calculated by the corrected linear-response IEFPCM (cLR-IEFPCM) approximation,55,56 but linear-response57 (LR-)IEFPCM results are reported in the SI). All KS-DFT and LR-KS-TDDFT calculations were carried out with the Gaussian 09 (rev. E.01) suite of programs.58 An ultrafine integration grid was employed in all cases. Natural transition orbitals (NTOs)59 were computed from the transition densities between the electronic ground-state and each excited state of interest. Plots and figures were produced with the help of Gnuplot 5.0, Vesta60 and Luscus.61 Orbitals are depicted with a surface isodensity value of 0.35 a.u. 2.2 MCSCF Multiconfiguration self-consistent field (MCSCF) calculations were carried in both state-specific (SS) and state-averaged (SA)62 modes. The SA calculations will be labeled SA(n) where n is the number of



Page 8 of 35

8 roots averaged over. We used both complete active spaces (CASSCF31) and restricted active spaces (RASSCF32). Complete active spaces are labelled (n,o), where n is the number of active electrons, and o is the number of active orbitals, and CASSCF calculations include all configurations that can be generated with this choice of n and o, with inactive electrons in doubly occupied orbitals. The active and inactive orbitals are optimized simultaneously with the configuration interaction (CI) coefficients. Restricted active spaces are labelled (n,h,p;o1,o2,o3), where the n electrons (in total) are distributed in o1 orbitals of a RAS1 subspace, o2 orbitals of a RAS2 subspace, and o3 orbitals of a RAS3 subspace. The subspaces are defined such that up to h holes are allowed in RAS1, and up to p particles are allowed to be excited to RAS3, whereas all electronic configurations are allowed within RAS2. As in CASSCF, RASSCF calculations optimize both the orbitals and CI coefficients. RASCI is like RASSCF except that the orbitals are not optimized (the orbitals are from a previous calculation and only the CI coefficients are optimized). Atomic natural orbital (ANO) basis-sets63,64 were used. The ANO-S-MB minimal basis was used to explore possible active space choices, and the relativistic ANO-RCC-VDZP basis set was used for production calculations. Molecular spatial symmetry was not imposed. Default computational parameters were used except for the total energy convergence threshold of SARASSCF orbital optimizations with ten roots, which was set to 10-6 a.u. (rather than the default 10-8 a.u.) due to convergence problems. All MCSCF and post-MCSCF calculations were carried out with Molcas 8.2.65 2.3 Post-MCSCF calculations


Page 9 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


9 Post-MCSCF calculations were carried out by both wave function theory (WFT) and pair-density functional theory (MC-PDFT28). A key feature of the present study is the use of restricted active space configuration interaction (RASCI) wave functions. Such calculations involve the optimization of the CI coefficients, but not orbital optimization. The orbitals are taken from a previous MCSCF calculation with a less demanding active space. Wave function post-SCF calculations were also carried out by single-state restricted-active-space second-order perturbation theory (SS-RASPT234), multi-state complete-active-space second-order perturbation theory (MS-CASPT2),66 and RASCI-PT2. For PT2 calculations, we used the standard IPEA shift of 0.25 a.u.67 and an imaginary shift68 of 0.2 a.u. The Cholesky decomposition (CD) algorithm, as implemented in Molcas,69 has been employed throughout. The MC-PDFT calculations employed both translated and fully translated functionals: tPBE, ftPBE, and ftBLYP.28,36 RASCI-PDFT calculations are denoted RASCI-X, where X = tPBE, ftPBE, or ftBLYP. 2.4 Spectral line broadening Vibrational broadening was added to the vertical transitions by the Franck-Condon displaced harmonic oscillator (FC-DHO) model as implemented in the FCBand software (version 2017B).70 Gas-phase CAM-B3LYP calculations were used to generate the frequencies and excited-state gradients for all FCDHO calculations.

3. Results and Discussion 3.1 Structures



Page 10 of 35

10 The ground-state electronic configurations of the molecules are closed-shell singlets. Optimizations in DMF solvent lead to structures very close to those obtained in the gas phase. The final coordinates of ground-state structures both in the gas phase and in DMF are reported in the SI (Tables S12-S15 of the SI). The presence of single C—C bonds and the steric hindrance imposed by ligand groups lead to nonplanar geometries; 1-DINAPH has a slight bending of the dihydrophenazine moiety (see SI, Figure S1) inwards, towards the farthest end of naphthyl groups, whereas 2-DINAPH has this bending outward.

3.2 KS-DFT Figures 2a-2b show the simulated UV-Visible absorption spectra in the gas-phase and in DMF (FCDHO/cLR-IEFPCM/CAM-B3LYP), and it compares them with the experimental spectrum, which was digitized from Ref.21 The experimental bands for both compounds are shifted to the red by about 0.5 eV as compared to theory. In both cases, the difference between gas-phase and solution-phase excitation energies is minimal, although the calculated oscillator strength is about a factor of 2 larger in solution (not seen in the figure because of the normalization employed in the figure). The main vertical excitation (S4←S0) resulting from gas-phase calculations, instead, is closer to the experimental value than is the solution-phase calculation (see also Table 1). The natural transition orbitals mainly involved in the bright transitions are shown in Figure 3 for 1-DINAPH and in Figure 4 for 2-DINAPH (the groundstate KS-DFT molecular orbitals are reported in Figures S3-S4 of the SI). All bright transitions are of ππ* type, and the main transitions involve similar orbitals, both in the gas phase and in DMF. The calculations can be used for assigning the bands. For 2-DINAPH, a lower-energy, weaker bright excitation (S2←S0) arises at 3.61 eV, and seems to correspond to the long tail of the main band of the experimental spectrum that goes from ca. 3.2 eV to 2.7 eV. The highest energy bright singlet of 2DINAPH will be indicated as S7, taking cLR-IEFPCM as reference. The HONTO (highest-occupied


Page 11 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


11 natural transition orbital) is localized on the dihydrophenazine part of the molecule, and the excitations can be characterized from the orbitals of Figures 3 and 4 as charge transfer (CT) from dihydrophenazine to ligand (1-DINAPH, see Fig. 3a), local excitations (LE) on the dihydrophenazine (1-DINAPH, Fig. 3a), or mixed CT/LE character (1-DINAPH – Fig. 3b – and 2-DINAPH, Fig. 4a-4b). All bright singlet excitations have non-negligible coefficients for both CT and LE excitations; i.e., they have a mixed CT/LE character (Table 1), if ground-state KS-DFT orbitals are considered (see Figures S3-S4). This picture is greatly simplified through the use of natural transition orbitals, which provide a consistent framework for the study of electronic excitations. As a first observation, for all transitions the only orbitals involved are HONTO and LUNTO, with amplitude values close to 1. Second, the KS-DFT picture is qualitatively correct, but NTOs better highlight the mixed CT/LE nature of bright excitations, and they also show a difference between gas-phase and solution-phase excitations for 1-DINAPH. In fact, whereas both S4 and S7 have a mixed CT/LE character in the gas phase, the implicit solvation model with DMF (which is a very polar solvent with dielectric constant 37.219) perturbs the electron density, leading to more localized transitions that are mostly of LE type for S4 and of CT type for S7. In the case of 2-DINAPH, the S2 transition (Figure 4b) is purely CT, although the oscillator strength (f = 0.0025) indicates that it is weakly bright.



Page 12 of 35

12

Figure 2. Simulated (FC-DHO/cLR-IEFPCM/CAM-B3LYP) vs. experimental UV-Visible absorption spectra of a) 1-DINAPH and b) 2-DINAPH in DMF. The main bands in the theoretical results are labelled by the dominating contributing excitation. Each curve is normalized to the same maximum for comparison of the positions and shapes. A figure showing also the LR-IEFPCM spectrum is reported in the SI (Figure S5).

Table 1. Bright singlets, largest excitation amplitudes (H = HOMO, L = LUMO), vertical excitation energies (eV), and oscillator strengths for 1-DINAPH and 2-DINAPH in gas-phase and in DMF solvent (cLR-IEFPCM/CAM-B3LYP). Excitations amplitudes are ordered by decreasing magnitude. gas phase, theorya

DMF, theoryb


DMF, Exp.c

Page 13 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


13 Sn

Orbitals

|coeff.|

∆E

f

Orbitals

|coeff.|

∆E

f

∆E

H→L+3

0.60

3.96

0.100

H→L+3

0.55

3.97

0.222

3.43

H→L+9

0.29

H→L+6

0.40

H→L+11

0.14

H-3→L+2

0.12

H-1→L+2

0.13 4.40

0.084

3.61

0.025

4.04

0.159

4.55

0.108

1-DINAPH 4

7

H→L+9

0.53

H→L+6

0.54

H→L+3

0.35

4.40

0.097

H→L+3

0.42

H→L+11

0.21

H-3→L+4

0.13

H-1→ L+6

0.16 H→L+1

0.66

H→L+6

0.19

H-3→L

0.12

2-DINAPH 2

4

7

H→L+2

0.62

H→L+2

0.58

H→L+12

0.19

H→L+6

0.27

H→L+8

0.15

H→L+9

0.18

H→L+16

0.12

H-3→L+3

0.12

H-1→L+3

0.12

H→L+12

0.39

H→L+8 H→L+2

3.97

0.071

H→L+15

0.11

H→L+6

0.48

0.38

H→L+2

0.35

0.27

H→L+9

0.23

4.47

0.109

H→L+16

0.24

H→L+1

0.17

H-1→L+5

0.17

H-3→L+4

0.14

H→L+1

0.15

H→L+15

0.13

a CAM-B3LYP b cLR-IEFPCM/CAM-B3LYP c Ref. 21 (λ

max

: 362 nm for 1-DINAPH and 340 nm for 2-DINAPH)


3.65


Page 14 of 35

14

Figure 3. CAM-B3LYP bright transitions for 1-DINAPH computed a) in gas-phase and b) in DMF solvent (by using the cLR-IEFPCM method). The HONTO orbital is visually indistinguishable among different excitations, thus only one is reported. H = HONTO, L = LUNTO.


Page 15 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


15

Figure 4. CAM-B3LYP bright transitions for 2-DINAPH computed a) in gas-phase and b) in DMF solvent (by using the cLR-IEFPCM method). The HONTO orbital is visually indistinguishable among different excitations, thus only one is reported. H = HONTO, L = LUNTO. 3.3 SA-CASSCF calculations State-averaged CASSCF calculations were carried out for both 1-DINAPH and 2-DINAPH excited states. Various active spaces were tested. An (8,12) active space – i.e. 8 electrons in 12 π-type orbitals (four occupied, the four correlating unoccupied ones and four more unoccupied orbitals). Combined with an average over the lowest ten roots (S0 to S9), this active space gave highly symmetric orbitals similar to those obtained from KS-DFT. Details of how possible active spaces were searched are given in SI (page S-14) along with vertical excitation energies and oscillator strengths by CAS-PDFT calculations with the tPBE on-top density functional and SS-CASPT2 and MS-CASPT2. They will not be dis-



Page 16 of 35

16 cussed here because the results do not agree well with experiment. We conclude that an (8,12) active space is not balanced because it includes orbitals with low occupation numbers because of their role in excitations, but it excludes important correlating orbitals. We thus considered larger active spaces. 3.4 SA- Active space selection and orbitals for RASCI and post-RASCI calculations Including of all π and π* valence orbitals (32 for 1- and 2-DINAPH) in CASSCF calculations or even in RASSCF calculations allowing a significant number of orbitals in RAS2 is practically beyond reach. Therefore, we employed a RASCI strategy. In particular, we built an active space with 24 orbitals by successive RASCI-based calculations for both molecules. The active space search protocol was as follows: •

We carried out an SS-RASSCF orbital optimization on the electronic ground state starting from the Hartree–Fock orbitals and including 32 electrons in all the 32 π and π* orbitals. RAS2 was excluded, but two holes in RAS1 and two electrons in RAS3 were allowed. This corresponds to a (32,2,2;16,0,16) active space.

•

We then carried out an SA(5)-RASSCF with the same active space by taking the SS-RASSCF ground-state orbitals as input.

•

Using the orbitals optimized from the previous step, another SA(10)-RASSCF (32,2,2;16,0,16) calculation was carried out, this time including ten roots in the state-averaging procedure. This active space generates 33153 configuration state functions (CSFs). Because RAS2 is excluded, the wave function description is still poor, but this calculation serves well to select the orbitals for subsequent calculations with a smaller active space, but including orbitals in RAS2. In particular, eliminating four active orbitals with state-averaged occupation numbers greater than 1.98 and the four corresponding antibonding ones (which have occupation numbers ≤0.02) leaves 24 active orbitals to be used for subsequent steps.


Page 17 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


17 •

We then carried out RASCI calculations with a (24,2,2;11,8,5) active space, which has 24 electrons in 24 orbitals. In this step RAS2 was included, and it contains 8 orbitals. The total number of CSFs for this active space is 280085. The active orbitals for 1-DINAPH and 2-DINAPH, respectively, are reported in Fig. S8-S9 of the SI. The number and type of orbitals in each subspace was chosen based on occupation numbers in the SA(10)-RASSCF(32,2,2;16,0,16) calculation, on including important correlating orbitals, and on orbital symmetry. Two holes were allowed in RAS1 and two particles were allowed in RAS3.

•

The RASCI-PT2 oscillator strengths are calculated from the RASCI-PT2 transition energy combined with the RASCI transition dipole, and the RASCI-PDFT oscillator strengths are calculated from the RASCI-PDFT transition energy combined with the RASCI transition dipole.

3.5 RASCI and post-RASCI calculations The RASCI wave function of the previous section was then used as a starting point for RASCI-PT2 calculations, and the RASCI density and on-top density were used for RASCI-PDFT calculations. Table 2 reports the RASCI vertical excitation energies and oscillator strengths computed for 1-DINAPH and 2-DINAPH and compares them with LR-KS-TDDFT/CAM-B3LYP, RASCI-tPBE and SS-RASCI-PT2 energies. (SS-CASPT2 and MS-CASPT2 calculations based on CASSCF (8,12) are reported in the SI, Table S8). In Table 2 the energies are ordered such that we compare energies related to the same RASCI state. The mean deviations from RASCI-PT2 are reported with this ordering in Table 2, and they show that, for both compounds, both RASCI-tPBE and CAM-B3LYP agree with RASCI-PT2. This is especially noteworthy because the deviation from RASCI is very large – more than 3 eV on average. Although both RASCI-tPBE and CAM-B3LYP perform well for excitation energies, RASCI-tPBE would perform relatively better if the excitations were ordered by energy.



Page 18 of 35

18 Table 2. 1-DINAPH and 2-DINAPH vertical singlet transition energies and oscillator strengths (theoretical results in the gas phase, experiment in DMF solution). Results for the brightest transition are bold. 1-DINAPH RASCI

RASCI-tPBE RASCI-PT2 CAM-B3LYP RASCI RASCI-tPBE RASCI-PT2 CAM-B3LYP

State

Energy (eV) Energy (eV)

Energy (eV)

Energy (eV)

S1

6.08

2.81

3.15

3.16

S2

6.17

3.36

3.21

3.16

S3

6.25

2.94

3.24

3.53

S4

6.58

3.43

3.63

3.96

0.585

0.687

0.485

0.100

S5

7.04

3.78

3.86

4.25

0.0003

0.0004

0.0003

0.0011

S6

7.33

4.28

4.14

4.26

S7

7.34

4.19

4.20

4.40

0.112

0.144

0.096

0.097

Expt. MDa

f

f

f

f

0.011

0.013

0.008

0.0000

0.9b

3.42 3.05

MUDa 3.05

-0.09

0.18

0.17

0.20

2-DINAPH RASCI

RASCI-tPBE RASCI-PT2 CAM-B3LYP RASCI RASCI-tPBE RASCI-PT2 CAM-B3LYP

State

Energy (eV) Energy (eV)

Energy (eV)

Energy (eV)

S1

6.56

3.00

3.35

3.41

S2

6.68

3.41

3.53

3.44

S3

6.93

3.41

3.67

3.71

S4

7.22

3.64

3.79

3.97

0.218

S5

7.37

3.95

4.00

4.21

0.007

S6

7.65

4.46

4.25

4.29

S7

7.69

4.28

4.37

4.47

0.075

0.094

Expt. a

MD

f

f

f

f

0.100

0.115

0.079

0.008

0.247

0.171

0.071

0.009

0.006

0.0000

0.064

0.110

0.65

3.65 3.30

MUDa 3.30

-0.12

0.08

0.18

0.10

b

a MD and MUD denote mean deviation and mean unsigned deviation with respect to the RASCI-PT2 result, taken as reference. b These numbers refer to the experimental normalized intensities reported in arbitrary units (Ref .21) Though they cannot directly be compared to theoretical oscillator strengths, they show the relative absorption intensity between the two systems.


Page 19 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


19 RASCI-tPBE gives the energy of the bright state very close to that inferred from experiment (3.43 eV vs. 3.42 eV for 1-DINAPH; 3.64 eV vs. 3.65 eV for 2-DINAPH). We should keep in mind that the latter is measured in DMF solvent; however, it was discussed above that implicit solvation does not have a large effect on the absorption spectrum. The computed UV-Visible spectra are depicted in Figures 5 and 6.

Figure 5. 1-DINAPH simulated UV-Visible absorption spectra from gas-phase post-RASCI calculations vs. gas-phase CAM-B3LYP and solution-phase experiment.



Page 20 of 35

20 Figure 6. 2-DINAPH simulated UV-Visible absorption spectra from gas-phase post-RASCI calculations vs. gas-phase CAM-B3LYP and solution-phase experiment. Concerning the oscillator strengths, those given by RASCI-tPBE are much more consistent with those of RASCI-PT2, with respect to the CAM-B3LYP ones in gas-phase. This is partly due to the fact that RASCI-tPBE and RASCI-PT2 oscillator strengths are calculated from the transition dipole moments (see Tables S9 and S10 of the SI for the different dipole strengths given by Molcas) provided by the same RASCI wave function. By analyzing the character of the excitations (Figures 7 and 8, and Table 3) we observed that the CAM-B3LYP and RASCI wave functions are qualitatively consistent. First, the ground state is unarguably of single-reference character, whereas other excited singlets are inherently multiconfigurational. Next consider S1 of 1-DINAPH: this is dominated by a HONTO→LUNTO CT transition with CAMB3LYP. RASCI predicts, besides the same CT transition (HONO→LUNO) (NO = natural orbital) with low configuration weight (0.24), another transition (HONO→LUNO+4, weight: 0.54) in which the LUNO+4 orbital is delocalized over the whole molecule. Thus, the dark S1 excitation thus becomes a mixed CT/LE transition according to RASCI. The bright excitations (S4 and S7) are described by the same kind of transitions, which are mixed for both states in the case of CAM-B3LYP, whereas RASCI gives a dominant configuration for each state (LE for S4 and CT for S7). This is in better agreement with what is observed for CAM-B3LYP in liquid-solution phase (see Figure 3b).

In 2-DINAPH, the CAM-B3LYP dark S1 state is dominated by a single HONTO-LUNTO transition which is mostly of CT type (Figure 8). RASCI natural orbitals, on the other hand, present a transition which is of mixed CT/LE character, more localized on the dihydrophenazine core. Unlike 1-DINAPH, the bright excitations of 2-DINAPH have markedly multiconfigurational character. In the case of


Page 21 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


21 RASCI calculations, mixed CT/LE bright transitions arise from the combination of pure CT and LE configurations, whereas CAM-B3LYP transitions are delocalized over the whole molecule.

Figure 7. 1-DINAPH CAM-B3LYP (left) and RASCI (right) orbitals involved in the S1 dark excitation and in the bright excitations (S2 and S5, from Table 3, are considered weak and they are not shown). For RASCI, the weight of each configuration is reported. H=HONTO/HONO, L=LUNTO/ LUNO.



Page 22 of 35

22

Figure 8: 2-DINAPH CAM-B3LYP (left) and RASCI (right) orbitals involved in the S1 dark excitation and in the bright excitations (S5, from Table 3, is considered weak and it is not shown). For RASCI, the weight of each configuration is reported. H=HONTO/HONO, L=LUNTO/LUNO.

As summarized by Table 3, most dark states have a multiconfigurational character, as well as the bright states of 2-DINAPH. 1-DINAPH, in contrast, has bright states with a more pronounced singlereference character. All main RASCI configurations involved in the excited states come from the RAS2 active space. One could wonder (against rational hope) if a CASSCF comprising only these eight orbitals (Figures S6 and S7 of the SI) – i.e. CAS (2,8) – would lead to the same results and to quantitative vertical excitation energies after the addition of dynamical correlation. We tried this for 1-DINAPH (Table S11); as expected, CAS-tPBE (2,8) results are markedly deteriorated (about 1 eV difference with respect to previous RASCI-PT2 results) by the appearance of Rydberg-like spurious orbitals (see SI, Figure S10). We observed that active spaces with an unbalanced number of bonding and antibonding orbitals lead to highly


Page 23 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


23 mixed and nonsymmetric orbitals (for example in the CAS(2,8) case some spurious Rydberg-like orbitals are present into the active space). This also holds also for spaces that in principle should be ‘balanced’ such as (12,12) or (16,16) where not all the important correlated orbitals are considered. The RASCI-PDFT calculations discussed so far are of RASCI-tPBE type. We also computed RASCIftPBE and RASCI-ftBLYP vertical excitation energies, and the results are reported in Table 4 (the absorption spectra are reported in Figure S11 of the SI). The mean signed and unsigned deviations from RASCI-PT2 (MD/MUD: -0.13/0.21 eV for both functionals) are slightly larger than for RASCI-tPBE (MD/MUD: -0.09/0.17 eV). There is a large difference between RASCI-PDFT and the LR-KS-TDDFT calculations with the parent functionals; for example, PBE energies are underestimated by ~1.4 eV, whereas the corresponding tPBE and ftPBE energies are underestimated only by ~0.1–0.2 eV. Table 3. 1-DINAPH and 2-DINAPH configurations from RASCI, with the related CI coefficients and weights (only configurations with weight > 0.10 are reported). 1-DINAPH

2-DINAPH

State

Configuration

Weighta

Configuration

Weighta

S0

222222222222000000000000

0.81

222222222222000000000000

0.81

22222222222u0d0000000000

0.73

22222222222ud00000000000

0.11

22222222222u000d00000000

0.20

22222222222u00000d000000

0.48

S1 S2

S3

S4

22222222222ud00000000000

0.24

22222222222u0000d0000000

0.54

22222222222u0d0000000000

0.69

22222222222ud00000000000

0.50

22222222222u00d000000000

0.35

22222222222u00d000000000

0.15

22222222222u0000d0000000

0.45

22222222222u0000d0000000

0.15

22222222222u000000d00000

0.70

22222222222ud00000000000

0.15

22222222222u000d00000000

0.35

22222222222u00000d000000

0.27

S5

22222222222u00000d000000

0.76

22222222222u000000d00000

0.77

S6

22222222222u00d000000000

0.62

22222222222u00d000000000

0.39

22222222222u0000d0000000

0.12

22222222222u0000d0000000

0.35

22222222222u000d00000000

0.75

22222222222ud00000000000

0.54

22222222222u000d00000000

0.25

S7

a The weight is the square of the configuration interaction coefficient.



Page 24 of 35

24

The tPBE UV-Visible absorption spectra agrees well with the experimental one. If the small difference between absorption in gas-phase and in solution obtained using cLR/CAM-B3LYP were valid also for RASCI-tPBE, then RASCI-tPBE would be slightly more accurate than RASCI-PT2.

Table 4: 1-DINAPH and 2-DINAPH gas-phase vertical transition energies (eV) from LR-KSTDDFT (PBE functional), RASCI-PDFT (tPBE, ftPBE and ftBLYP functionals) compared to RASCIPT2a 1-DINAPH

2-DINAPH

State

PBE

RASCItPBE

RASCIftPBE

RASCIftBLYP

RASCIPT2

PBE

RASCItPBE

RASCIftPBE

RASCIftBLYP

RASCIPT2

S1

1.42

2.81

2.74

2.75

3.15

1.60

3.00

2.92

2.92

3.35

S2

1.42

3.36

3.36

3.37

3.21

1.60

3.41

3.38

3.38

3.53

S3

2.22

2.94

2.87

2.88

3.24

2.37

3.41

3.35

3.35

3.67

S4

2.23

3.43

3.38

3.37

3.63

2.40

3.64

3.58

3.58

3.79

S5

2.83

3.78

3.72

3.70

3.86

2.81

3.95

3.89

3.86

4.00

S6

2.89

4.28

4.27

4.28

4.14

3.10

4.46

4.45

4.46

4.25

S7

2.90

4.19

4.18

4.19

4.20

3.11

4.28

4.26

4.25

4.37

MD

-1.36

-0.09

-0.13

-0.13

-1.42

-0.12

-0.16

-0.17

MUD

1.36

0.17

0.21

0.21

1.42

0.18

0.22

0.23

a MD and MUD denote mean deviation and mean unsigned deviation with respect to the RASCI-PT2 result, taken as reference.

3.6 RASCI-PDFT computational cost In terms of computational time, the post-RASCI step of RASCI-PDFT calculations for a single root required on average 178 minutes per processor (Intel Xeon CPU [email protected], GNU/Linux x86_64 cluster architecture), whereas the post-RASCI step of RASCI-PT2 required 1259 minutes per processor, a factor of 7 slower.


Page 25 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25

4. Conclusions We investigated the behaviour of the singlet excited states of two organic fluorescent photoredox catalysts. The mixed CT/LE behaviour of the vertical bright transitions was unveiled with the help of singlereference and multi-reference quantum mechanical electronic structure calculations, and the lowest singlet excited state is confirmed to be dark. Though CAM-B3LYP is able to capture the orbital nature and energy for the most important transitions, it misses their partly multiconfigurational character. Multireference RASCI-PDFT calculations provide an accurate description of the experimental optical absorption spectra – both excited-state energies and oscillator strengths – compared to both RASCI-PT2 at a significantly lower cost. These results were achieved by the inclusion of all valence orbitals in the active space and their optimization within a cost-effective computational protocol consisting of RASSCF calculations without a RAS2 active subspace followed by RASCI calculations with an overall smaller number of orbitals in the active space, but that include some orbitals in RAS2. This approach to generate a reference wave function for MC-PDFT calculations allowed us to systematically control the orbitals included in the active space, and it can be extended more generally to other classes of systems.

Associated Content Supporting Information. Structural parameters, excited-state properties, active space search protocol, ground-state KS-DFT orbitals, CASSCF orbitals, RASSCF orbitals, RASCI dipole and velocity transition strengths, CASSCF/tPBE (2,8) orbitals and energies, UV/Vis. spectra, optimized geometries, input text-files of RASCI orbitals and complete references 58 and 65.



Page 26 of 35

26

Author Information Corresponding Authors: E-mail: [email protected]; [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

Acknowledgements We thank R. K. Carlson, C. E. Hoyer, and S. Ghosh for helpful advice. This work was supported in part by AFOSR grant FA9550-16-1-0134.

References (1)

G. Bünzli, J.-C.; Piguet, C. Taking Advantage of Luminescent Lanthanide Ions. Chem. Soc. Rev. 2005, 34, 1048–1077.

(2)

Baldo, M. A.; O’Brien, D. F.; You, Y.; Shoustikov, A.; Sibley, S.; Thompson, M. E.; Forrest, S. R. Highly Efficient Phosphorescent Emission from Organic Electroluminescent Devices. Nature 1998, 395, 151–154.

(3)

Burroughes, J. H.; Bradley, D. D. C.; Brown, A. R.; Marks, R. N.; Mackay, K.; Friend, R. H.; Burns, P. L.; Holmes, A. B. Light-Emitting Diodes Based on Conjugated Polymers. Nature 1990, 347, 539–541.


Page 27 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


27 (4)

de Silva, A. P.; Gunaratne, H. Q. N.; Gunnlaugsson, T.; Huxley, A. J. M.; McCoy, C. P.; Rademacher, J. T.; Rice, T. E. Signaling Recognition Events with Fluorescent Sensors and Switches. Chem. Rev. 1997, 97, 1515–1566.

(5)

Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphry-Baker, R.; Mueller, E.; Liska, P.; Vlachopoulos, N.; Graetzel, M. Conversion of Light to Electricity by Cis-X2bis(2,2’-Bipyridyl-4,4’Dicarboxylate)Ruthenium(II) Charge-Transfer Sensitizers (X = Cl-, Br-, I-, CN-, and SCN-) on Nanocrystalline Titanium Dioxide Electrodes. J. Am. Chem. Soc. 1993, 115, 6382–6390.

(6)

Medintz, I. L.; Uyeda, H. T.; Goldman, E. R.; Mattoussi, H. Quantum Dot Bioconjugates for Imaging, Labelling and Sensing. Nat. Mater. 2005, 4, 435–446.

(7)

Nakamura, S. The Roles of Structural Imperfections in InGaN-Based Blue Light-Emitting Diodes and Laser Diodes. Science 1998, 281, 956–961.

(8)

Pavesi, L.; Negro, L. D.; Mazzoleni, C.; Franzò, G.; Priolo, F. Optical Gain in Silicon Nanocrystals. Nature 2000, 408, 440–444.

(9)

Grätzel, M. Photoelectrochemical Cells. Nature 2001, 414, 338–344.

(10) Günes, S.; Neugebauer, H.; Sariciftci, N. S. Conjugated Polymer-Based Organic Solar Cells. Chem. Rev. 2007, 107, 1324–1338. (11) Huang, X.; Han, S.; Huang, W.; Liu, X. Enhancing Solar Cell Efficiency: The Search for Luminescent Materials as Spectral Converters. Chem. Soc. Rev. 2013, 42, 173–201. (12) Asahi, R.; Morikawa, T.; Ohwaki, T.; Aoki, K.; Taga, Y. Visible-Light Photocatalysis in Nitrogen-Doped Titanium Oxides. Science 2001, 293, 269–271. (13) Kudo, A.; Miseki, Y. Heterogeneous Photocatalyst Materials for Water Splitting. Chem. Soc. Rev. 2009, 38, 253–278.



Page 28 of 35

28 (14) Wang, X.; Maeda, K.; Thomas, A.; Takanabe, K.; Xin, G.; Carlsson, J. M.; Domen, K.; Antonietti, M. A Metal-Free Polymeric Photocatalyst for Hydrogen Production from Water under Visible Light. Nat. Mater. 2008, 8, 76–80. (15) Brédas, J.-L.; Beljonne, D.; Coropceanu, V.; Cornil, J. Charge-Transfer and Energy-Transfer Processes in π-Conjugated Oligomers and Polymers: A Molecular Picture. Chem. Rev. 2004, 104, 4971–5004. (16) Presti, D.; Labat, F.; Pedone, A.; Frisch, M. J.; Hratchian, H. P.; Ciofini, I.; Menziani, M. C.; Adamo, C. Computational Protocol for Modeling Thermochromic Molecular Crystals: Salicylidene Aniline As a Case Study. J. Chem. Theory Comput. 2014, 10, 5577–5585. (17) Grabowski, Z. R.; Rotkiewicz, K.; Rettig, W. Structural Changes Accompanying Intramolecular Electron Transfer: Focus on Twisted Intramolecular Charge-Transfer States and Structures. Chem. Rev. 2003, 103, 3899–4032. (18) Presti, D.; Labat, F.; Pedone, A.; Frisch, M. J.; Hratchian, H. P.; Ciofini, I.; Cristina Menziani, M.; Adamo, C. Modeling Emission Features of Salicylidene Aniline Molecular Crystals: A QM/QM’ Approach. J. Comput. Chem. 2016, 37, 861–870. (19) Presti, D.; Pedone, A.; Ciofini, I.; Labat, F.; Menziani, M. C.; Adamo, C. Optical Properties of the Dibenzothiazolylphenol Molecular Crystals through ONIOM Calculations: The Effect of the Electrostatic Embedding Scheme. Theor. Chem. Acc. 2016, 135, 86. (20) Presti, D.; Wilbraham, L.; Targa, C.; Labat, F.; Pedone, A.; Menziani, M. C.; Ciofini, I.; Adamo, C. Understanding Aggregation-Induced Emission in Molecular Crystals: Insights from Theory. J. Phys. Chem. C 2017, 121, 5747–5752.


Page 29 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


29 (21) Theriot, J. C.; Lim, C.-H.; Yang, H.; Ryan, M. D.; Musgrave, C. B.; Miyake, G. M. Organocatalyzed Atom Transfer Radical Polymerization Driven by Visible Light. Science 2016, 352, 1082– 1086. (22) Lim, C.-H.; Ryan, M. D.; McCarthy, B. G.; Theriot, J. C.; Sartor, S. M.; Damrauer, N. H.; Musgrave, C. B.; Miyake, G. M. Intramolecular Charge Transfer and Ion Pairing in N,N-Diaryl Dihydrophenazine Photoredox Catalysts for Efficient Organocatalyzed Atom Transfer Radical Polymerization. J. Am. Chem. Soc. 2017, 139, 348–355. (23) Matyjaszewski, K. Atom Transfer Radical Polymerization (ATRP): Current Status and Future Perspectives. Macromolecules 2012, 45, 4015–4039. (24) Ryan, M. D.; Theriot, J. C.; Lim, C.-H.; Yang, H.; G. Lockwood, A.; Garrison, N. G.; Lincoln, S. R.; Musgrave, C. B.; Miyake, G. M. Solvent Effects on the Intramolecular Charge Transfer Character of N,N-Diaryl Dihydrophenazine Catalysts for Organocatalyzed Atom Transfer Radical Polymerization. J. Polym. Sci. Part Polym. Chem. 2017, 55, 3017–3027. (25) Dreuw, A.; Head-Gordon, M. Failure of Time-Dependent Density Functional Theory for LongRange Charge-Transfer Excited States: The Zincbacteriochlorin−Bacteriochlorin and Bacteriochlorophyll−Spheroidene Complexes. J. Am. Chem. Soc. 2004, 126, 4007–4016. (26) Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid Exchange–correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51–57. (27) Song, J.-W.; Tokura, S.; Sato, T.; Watson, M. A.; Hirao, K. An Improved Long-Range Corrected Hybrid Exchange-Correlation Functional Including a Short-Range Gaussian Attenuation (LCgauBOP). J. Chem. Phys. 2007, 127, 154109. (28) Li Manni, G.; Carlson, R. K.; Luo, S.; Ma, D.; Olsen, J.; Truhlar, D. G.; Gagliardi, L. Multiconfiguration Pair-Density Functional Theory. J. Chem. Theory Comput. 2014, 10, 3669–3680.



Page 30 of 35

30 (29) Gagliardi, L.; Truhlar, D. G.; Li Manni, G.; Carlson, R. K.; Hoyer, C. E.; Bao, J. L. Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems. Acc. Chem. Res. 2017, 50, 66–73. (30) Ghosh, S.; Sonnenberger, A. L.; Hoyer, C. E.; Truhlar, D. G.; Gagliardi, L. Multiconfiguration Pair-Density Functional Theory Outperforms Kohn–Sham Density Functional Theory and Multireference Perturbation Theory for Ground-State and Excited-State Charge Transfer. J. Chem. Theory Comput. 2015, 11, 3643–3649. (31) Roos, B. O.; Taylor, P. R.; Siegbahn, P. E. M. A Complete Active Space SCF Method (CASSCF) Using a Density Matrix Formulated Super-CI Approach. Chem. Phys. 1980, 48, 157–173. (32) Malmqvist, P. A.; Rendell, A.; Roos, B. O. The Restricted Active Space Self-Consistent-Field Method, Implemented with a Split Graph Unitary Group Approach. J. Phys. Chem. 1990, 94, 5477–5482. (33) Olsen, J.; Roos, B. O.; Jo/rgensen, P.; Jensen, H. J. A. Determinant Based Configuration Interaction Algorithms for Complete and Restricted Configuration Interaction Spaces. J. Chem. Phys. 1988, 89, 2185–2192. (34) Sauri, V.; Serrano-Andrés, L.; Shahi, A. R. M.; Gagliardi, L.; Vancoillie, S.; Pierloot, K. Multiconfigurational Second-Order Perturbation Theory Restricted Active Space (RASPT2) Method for Electronic Excited States: A Benchmark Study. J. Chem. Theory Comput. 2011, 7, 153–168. (35) Malmqvist, P. Å.; Pierloot, K.; Shahi, A. R. M.; Cramer, C. J.; Gagliardi, L. The Restricted Active Space Followed by Second-Order Perturbation Theory Method: Theory and Application to the Study of CuO2 and Cu2O2 Systems. J. Chem. Phys. 2008, 128, 204109.


Page 31 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


31 (36) Carlson, R. K.; Truhlar, D. G.; Gagliardi, L. Multiconfiguration Pair-Density Functional Theory: A Fully Translated Gradient Approximation and Its Performance for Transition Metal Dimers and the Spectroscopy of Re2Cl82–. J. Chem. Theory Comput. 2015, 11, 4077–4085. (37) Nakatani, N.; Guo, S. Density Matrix Renormalization Group (DMRG) Method as a Common Tool for Large Active-Space CASSCF/CASPT2 Calculations. J. Chem. Phys. 2017, 146, 094102. (38) Sun, Q.; Yang, J.; Chan, G. K.-L. A General Second Order Complete Active Space SelfConsistent-Field Solver for Large-Scale Systems. Chem. Phys. Lett. 2017, 683, 291–299. (39) Boguslawski, K.; Marti, K. H.; Reiher, M. Construction of CASCI-Type Wave Functions for Very Large Active Spaces. J. Chem. Phys. 2011, 134, 224101. (40) Li Manni, G.; Smart, S. D.; Alavi, A. Combining the Complete Active Space Self-Consistent Field Method and the Full Configuration Interaction Quantum Monte Carlo within a Super-CI Framework, with Application to Challenging Metal-Porphyrins. J. Chem. Theory Comput. 2016, 12, 1245–1258. (41) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (42) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158–6170. (43) Peverati, R.; Truhlar, D. G. Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation. J. Phys. Chem. Lett. 2011, 2, 2810–2817. (44) Chai, J.-D.; Head-Gordon, M. Systematic Optimization of Long-Range Corrected Hybrid Density Functionals. J. Chem. Phys. 2008, 128, 084106.



Page 32 of 35

32 (45) Dreuw, A.; Weisman, J. L.; Head-Gordon, M. Long-Range Charge-Transfer Excited States in Time-Dependent Density Functional Theory Require Non-Local Exchange. J. Chem. Phys. 2003, 119, 2943–2946. (46) Li, R.; Zheng, J.; Truhlar, D. G. Density Functional Approximations for Charge Transfer Excitations with Intermediate Spatial Overlap. Phys. Chem. Chem. Phys. 2010, 12, 12697–12701. (47) Peverati, R.; Truhlar, D. G. Quest for a Universal Density Functional: The Accuracy of Density Functionals across a Broad Spectrum of Databases in Chemistry and Physics. Phil Trans R Soc A 2014, 372, 20120476. (48) Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 1972, 56, 2257–2261. (49) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. Self‐consistent Molecular Orbital Methods. XXIII. A Polarization‐type Basis Set for Second‐row Elements. J. Chem. Phys. 1982, 77, 3654–3665. (50) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Self‐consistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions. J. Chem. Phys. 1980, 72, 650–654. (51) Cramer, C. J.; Truhlar, D. G. Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics. Chem. Rev. 1999, 99, 2161–2200. (52) Mennucci, B.; Cancès, E.; Tomasi, J. Evaluation of Solvent Effects in Isotropic and Anisotropic Dielectrics and in Ionic Solutions with a Unified Integral Equation Method: Theoretical Bases, Computational Implementation, and Numerical Applications. J. Phys. Chem. B 1997, 101, 10506–10517.


Page 33 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


33 (53) Scalmani, G.; Frisch, M. J. Continuous Surface Charge Polarizable Continuum Models of Solvation. I. General Formalism. J. Chem. Phys. 2010, 132, 114110. (54) Rappé, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard III, W. A.; Skiff, W. M. UFF, a Full Periodic Table Force Field for Molecular Mechanics and Molecular Dynamics Simulations. J. Am. Chem. Soc. 1992, 114, 10024–10035. (55) Caricato, M.; Mennucci, B.; Tomasi, J.; Ingrosso, F.; Cammi, R.; Corni, S.; Scalmani, G. Formation and Relaxation of Excited States in Solution: A New Time Dependent Polarizable Continuum Model Based on Time Dependent Density Functional Theory. J. Chem. Phys. 2006, 124, 124520. (56) Guido, C. A.; Jacquemin, D.; Adamo, C.; Mennucci, B. Electronic Excitations in Solution: The Interplay between State Specific Approaches and a Time-Dependent Density Functional Theory Description. J. Chem. Theory Comput. 2015, 11, 5782–5790. (57) Cammi, R.; Mennucci, B. Linear Response Theory for the Polarizable Continuum Model. J. Chem. Phys. 1999, 110, 9877–9886. (58) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; et al. Gaussian 09 Revision E.01; 2009. (59) Martin, R. L. Natural Transition Orbitals. J. Chem. Phys. 2003, 118, 4775–4777. (60) Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr. 2011, 44, 1272–1276. (61) Kovačević, G.; Veryazov, V. Luscus: Molecular Viewer and Editor for MOLCAS. J. Cheminformatics 2015, 7, 16.



Page 34 of 35

34 (62) Stålring, J.; Bernhardssonn, A.; Lindh, R. Analytical Gradients of a State Average MCSCF State and a State Average Diagnostic. Mol. Phys. 2001, 99, 103–114. (63) Widmark, P.-O.; Malmqvist, P.-Å.; Roos, B. O. Density Matrix Averaged Atomic Natural Orbital (ANO) Basis Sets for Correlated Molecular Wave Functions. Theor. Chim. Acta 1990, 77, 291– 306. (64) Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P.-O. Main Group Atoms and Dimers Studied with a New Relativistic ANO Basis Set. J. Phys. Chem. A 2004, 108, 2851–2858. (65) Aquilante, F.; Autschbach, J.; Carlson, R. K.; Chibotaru, L. F.; Delcey, M. G.; De Vico, L.; Fdez. Galván, I.; Ferré, N.; Frutos, L. M.; Gagliardi, L.; et al. Molcas 8: New Capabilities for Multiconfigurational Quantum Chemical Calculations across the Periodic Table. J. Comput. Chem. 2016, 37, 506–541. (66) Finley, J.; Malmqvist, P.-Å.; Roos, B. O.; Serrano-Andrés, L. The Multi-State CASPT2 Method. Chem. Phys. Lett. 1998, 288, 299–306. (67) Ghigo, G.; Roos, B. O.; Malmqvist, P.-Å. A Modified Definition of the Zeroth-Order Hamiltonian in Multiconfigurational Perturbation Theory (CASPT2). Chem. Phys. Lett. 2004, 396, 142– 149. (68) Forsberg, N.; Malmqvist, P.-Å. Multiconfiguration Perturbation Theory with Imaginary Level Shift. Chem. Phys. Lett. 1997, 274, 196–204. (69) Aquilante, F.; Lindh, R.; Bondo Pedersen, T. Unbiased Auxiliary Basis Sets for Accurate TwoElectron Integral Approximations. J. Chem. Phys. 2007, 127, 114107. (70) Li, S. L.; Truhlar, D. G. Franck–Condon Models for Simulating the Band Shape of Electronic Absorption Spectra. J. Chem. Theory Comput. 2017, 13, 2823–2830.


Page 35 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


35 TOC Graphics


Intramolecular Charge Transfer and Local Excitation in Organic

Recommend Documents