Simultaneous Prediction of the Energies of Qx and Qy Bands and

Article pubs.acs.org/JPCA

Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

Simultaneous Prediction of the Energies of Qx and Qy Bands and Intramolecular Charge-Transfer Transitions in Benzoannulated and Non-Peripherally Substituted Metal-Free Phthalocyanines and Their Analogues: No Standard TDDFT Silver Bullet Yet Rodion V. Belosludov,*,† Dustin Nevonen,‡ Hannah M. Rhoda,§ Jared R. Sabin,§ and Victor N. Nemykin*,‡,§ Downloaded via UNIV OF GOTHENBURG on December 19, 2018 at 00:52:43 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku Sendai 980-8577, Japan Department of Chemistry, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada § Department of Chemistry & Biochemistry, University of Minnesota Duluth, Duluth, Minnesota 55812, United States ‡

S Supporting Information *

ABSTRACT: An insight into the electronic structure of the metal-free, unsubstituted, and nonperipherally substituted with electron-donating groups tetraazaporphyrin (H2TAP), phthalocyanine (H2Pc), naphthalocyanine (H2Nc), anthracocyanine (H2Ac) platforms has been gained and discussed on the basis of experimental UV−vis and MCD spectra as well as density functional theory (DFT), time-dependent DFT (TDDFT), and semiempirical ZINDO/S calculations. Experimental data are suggestive of potential crossover behavior between the 11B2u and 11B3u excited states (in traditional D2h notation) around 800 nm. A large array of exchange-correlation functionals were tested to predict the vertical excitation energies in H2TAPs, H2Pcs, H2Ncs, and H2Acs both in gas phase and solution. In general, TDDFT-predicted energies of the Qx and Qy bands and the splitting between them correlate well with the amount of Hartree−Fock exchange present in a specific exchange-correlation functional with the long-range corrected LC-BP86 and LC-wPBE functionals providing the best agreement between theory and experiment. The pure GGA (BP86) exchange-correlation functional significantly underestimated, while long-range corrected LC-BP86 and LC-wPBE exchange-correlation functionals and semiempirical ZINDO/S method strongly overestimated the intramolecular charge-transfer (ICT) transitions experimentally observed for -OR, -SR, and -NR2 substituted at nonperipheral position phthalocyanines and their analogues in the 450−650 nm region. The hybrid CAM-B3LYP, PBE1PBE, and B3LYP exchange-correlation functionals were found to be much better in predicting energies of such ICT transitions. Overall, we did not find a single exchange-correlation functional that can accurately (MAD < 0.05 eV) and simultaneously predict the energies and the splittings of the Qx and Qy bands as well as energies of the ICT transitions in a large array of substituted and unsubstituted metal-free phthalocyanines and their benzoannulated analogues.

1. INTRODUCTION Significant interest in the chemistry and spectroscopy of phthalocyanines (Pcs) and their analogues primarily originates from their wide array of applications that vary from their traditional use as blue or green dyes and pigments1,2 to more recent applications in oxidative catalysis,3−6 photodynamic therapy of cancer,7−11 antimicrobial and antibacterial phototherapy,12−14 nanotechnology,15−17 chemical sensing,18−20 materials chemistry,21−24 and nonlinear optics.25−27 The majority of these applications are related to the unique optical © XXXX American Chemical Society

properties of Pcs and their analogues and specifically the intense, low-energy Q-band observed in the visible or NIR region, which represents the first excited state in systems with effective 4-fold symmetry. In the case of metal-free or lowsymmetry Pcs and their analogues, the doubly degenerate first excited state of 1Eu symmetry splits into two components with Received: August 7, 2018 Revised: November 26, 2018 Published: December 4, 2018 A

DOI: 10.1021/acs.jpca.8b07647 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Figure 1. Target metal-free Pcs and their analogues.

x- and y-polarization (keeping z-axis perpendicular to the macrocycle plane), which results in the splitting of the Q-band into Qx- and Qy-transitions.28,29 The energy of the Q-band(s) in Pcs and their analogues can be tuned up by two general methods: (i) by a stepwise increase or decrease of the aromatic π-system in Pcs by the addition or elimination of the annulated benzene rings in Pcs; (ii) by the introduction of substituents into the Pc core.30−34 In the first case, the Q-band position (or Q-band center taken as the average energy between Qx- and Qy-transitions) shifts by ∼100 nm going from tetraazaporphyrin (TAP) to Pc to 2,3-naphthalocyanine (Nc) to anthracocyanine (Ac) systems (Figure 1).30,31 In addition, when metalfree compounds are considered, it is commonly accepted that the Qx/Qy band splitting decreases with the increase of molecular size with H2Nc and H2Ac compounds having only a single Q-band, which represents accidentally degenerate 11B2u and 11B3u excited states (in traditional D2h symmetry notation).30 In the case of substituted Pcs and their analogues, electron-donating substituents at α-positions (nonperipheral

positions) are responsible for the 40−80 nm low-energy shift of the Q-band(s), while the Q-band(s) shift caused by the similar substituents at β-positions (peripheral positions) of the phthalocyanine core is quite small.32,35,36 This difference reflects a larger contribution of the α-carbons to the HOMO, which results in a larger destabilization of the HOMO by electron-donating groups.32,37 In the case of the metal-free compounds, Qx/Qy band splitting decreases with the decrease of their energies.30 Recently, one research group has shown that the UV−vis spectra of the H 2Nc tBu and H2 Ac Ph8 compounds have significantly split (230−250 cm−1) Qx and Qy bands in CCl4 solvent with a larger splitting observed for H2AcPh8, which contradicts the earlier assumptions.38 Moreover, the UV−vis spectrum of the H 2 (α-OiPent) 8 Ac compound reported in a polar THF solution again shows an unexpected splitting of the Qx- and Qy-bands observed at 980 and 954 nm.39 These new findings call for a re-examination of the electronic structures and excited states with accidental degeneracy in the metal-free Pcs and their analogues. B


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PBE1PBE57 (also known as hybrid PBE0, 25% of Hartee− Fock exchange), and CAM-B3LYP58 exchange-correlation functionals. In addition, for the gas-phase BP86 and B3LYPbased geometries, a semiempirical ZINDO/S method,59 which is popular in the phthalocyanine community, was also used for prediction of the excited-state energies. In order to explore an influence of the exchange-correlation functional geometries on the TDDFT-predicted vertical excitation energies, we also optimized geometries of all compounds using TPSSh/PCM and PBE1PBE/PCM approaches, thus allowing a comparison of TDDFT calculations for BP86/PCM geometry−BP86/ PCM TDDFT, TPSSh/PCM geometry−TPSSh/PCM TDDFT, B3LYP/PCM geometry−B3LYP/PCM TDDFT, and PBE1PBE/PCM geometry−PBE1PBE/PCM TDDFT pairs that cover exchange-correlation functionals from 0% of Hartree−Fock exchange to 25% of Hartee−Fock exchange. In addition, in order to explore an influence of a larger array of the exchange-correlation functionals toward prediction of the vertical excitation energies for a single geometry, we run a different set of test calculation of the Qx- and Qy- band energies in H2TAP, H2Nc, and H2(α-SMe)8Pc using BP86 gas-phase and B3LYP gas-phase geometries and BP86,52,53 B97D,60 M06HF,61 O3LYP,62 wB97XD,63 X3LYP,64 HSeh1PBE,65 CAM-B3LYP,58 M062X,66 BMK,67 wB97,68 LC-BP86,54 LCwPBE,54 wB97X,68 M06L,61 TPSS,55 and TPSSh55 methods. All compounds were optimized without any reduction in geometry except all X-(Alk)n or X-(Aryl)n groups (X = O, S, n = 1; X = N, n = 2) were replaced with −CH3 substituents and t-Bu groups replaced by the hydrogen atoms. In the case of tetrasubstituted Pcs, only one out of four possible positional isomers was modeled in order to avoid further symmetry reduction. This isomer has four substituents located in the most symmetric fashion (Figure 1). H2TAP, H2Pc, H2Nc, H2Ac, and H2(α-OMe)8Pc compounds were optimized in the highest possible D2h point group. H2(α-OMe)8Nc and H2(αOMe)8Ac compounds were optimized in the C2v point group, while H2(α-OMe)4Pc and H2(α-SMe)4Pc in the C2h point group. For H 2 (α-SMe) 8 Pc, it was found that the C 2v conformation is 4.4−5.3 kcal/mol more stable than the D2 symmetry conformation, and thus, only C2v geometries were used in the analysis; however, both geometries gave very similar results. Since the −NMe2 groups in H2(α-NMe2)4Pc compounds are not perfectly coplanar with the phthalocyanine core, two atropisomers were considered: α,α,α,α- and α,β,α,β-, which are energetically almost perfectly equivalent (the energy differences range between 0.06 and 0.28 kcal/mol). Both atropisomers of H2(α-NMe2)4Pc were optimized in the C1 point group. For all optimized geometries, vibronic frequencies were calculated in order to confirm minima on the potential energy surface of the corresponding macrocycles. The excitation energies were calculated by a TDDFT approach with the lowest 40−100 singlet excited states being considered in order to ensure that both Q- and B-band regions of the UV− vis spectra of Pcs and their analogues are covered. Taking into consideration the size of the target macrocycles, a mediumsized 6-31G(d) basis set69 was used for all atoms. Our70 and the other researchers71,72 test calculations suggested that the basis set increase to the 6-311G(d) and 6-311+G(d) size resulted in very minor changes of the calculated electronic structure and the vertical excitation energies in considered macrocycles. Single-point and TDDFT calculations were conducted using pure GGA BP86,52,53 three long-range corrected (LC-BP86, LC-wPBE,54 and CAM-B3LYP58), and

In addition, although the extra bands observed in the 400− 600 nm range for expanded Pcs were attributed to the lowintensity π−π* transitions,30,32,36 similar peaks observed in the case of α-substituted by the electron-donating groups Pcs can be dominated by intramolecular charge-transfer (ICT) bands that are originated from single-electron excitations of the donor-atom lone pair to the macrocycle-centered π* orbitals.37 The electronic structure of the metal-free Pcs and their analogues along with their UV−vis spectroscopy, specifically the Qx- and Qy- band energies and the degree of splitting of the Q-bands, was a subject for several studies by simple PPP,36,40,41 semiempirical ZINDO/S,30,42−44 time-dependent density functional theory (TDDFT),34,45,46 and SAC−CI methods.31,47 To the best of our knowledge, however, no systematic study has been simultaneously conducted on the prediction of the energies and the splitting of the Qx- and Qy-bands and the energies of the ICT transitions in both expanded and substituted metal-free Pcs and their analogues, which would compare both modern TDDFT and semiempirical approaches. Thus, in this paper, we present experimental UV−vis and MCD data for a large variety of Pcs and their analogues along with the TDDFT and ZINDO/S calculations, which address the following questions: (i) How accurate are theoretical methods in predicting of the Qx- and Qy-band positions in metal-free Pcs and their analogues? (ii) Can TDDFT and ZINDO/S methods predict the experimental trends in Qx/Qybands splitting; (iii) What is the nature of the low intensity bands observed between 400 and 600 nm in α-substituted by electron-donating groups Pcs? (iv) Can long-range corrected exchange-correlation functionals improve the agreement between experimental data and predicted vertical excitation energies in the target compounds?

2. EXPERIMENTAL SECTION Materials and Physical Measurements. All solvents were purified using standard procedures48 in order to eliminate any possible acid and moisture contamination. H2TAPtBu (1), H2PctBu (2), H2NctBu (8), H2(α-OC6H13)8Pc (6), and H2(αOBu)8Nc (9) were prepared using published procedures30,36,49 or purchased from commercial sources. H2(α-OCH3)4Pc, H2(α-SPh)4PctBu (5), and H2(α-NEt2)4PctBu (4) compounds were obtained from Professor Eugenii Lukyanets and a sample of H2(α-p-SC6H4tBu)8Pc was received from Professor Keiichi Sakamoto. UV−vis data were obtained on Jasco-720 or Cary 17 spectrophotometers. MCD data were recorded using an OLIS DCM 17 CD spectropolarimeter using 1.4 T DeSa magnet. The MCD spectra were measured in mdeg = [θ] and converted to Δε (M−1 cm−1 T−1) using the regular conversion formula: Δε = θ/(32 980 × Bdc), where B is the magnetic field, d is the path length, and c is the concentration.50 Complete spectra were recorded at room temperature in parallel and antiparallel directions with respect to the magnetic field. Computational Details. All computations were performed using Gaussian 0951 software packages running under Windows or UNIX OS. Geometries of all compounds were optimized using BP86 or B3LYP exchange-correlation functionals both in gas phase and solution. In all solution calculations, PCM approach and DCM solvent were used. Optimized geometries (labeled as BP86 geometry gas and B3LYP geometry gas for gas-phase calculations as well as BP86/PCM geometry and B3LYP/PCM geometry for solution calculations) were then used for TDDFT calculations using BP86,52,53 LC-wPBE,54 LC-BP86,54 TPSSh,55 B3LYP,56 C


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Figure 2. Experimental UV−vis and MCD spectra of investigated metal-free Pcs and their analogues in cm−1 scale. Experimental values for Q-band energies in nm scale are given on the corresponding UV−vis graphs.

several hybrid (TPSSh, 55 B3LYP, 56 and PBE1PBE57 ) exchange-correlation functionals. Theoretical spectra calculated by TDDFT approach were modeled using GaussView 5.0 software73 using an 800 cm−1 bandwidth in all cases.

analogues are shown in Figure 2 and Figures S1−S44 (Supporting Information). It is generally accepted that in the case of stepwise benzoannulation (i.e., in the H2TAP, H2Pc, H2Nc, and H2Ac sequence), the energy gap between the Qxand Qy- bands decreases and these two bands collapse into a single band in H2Nc and H2Ac compounds.38,74 Indeed, when the UV−vis spectra of H2NctBu (8) and H2ActBu (10) were collected in pyridine, only a single Q-band was experimentally observed in the low-energy region.30 In a different report, however, one research group has shown that the Q-band splits into two closely spaced Qx- and Qy-components when the UV−vis spectra of the H2NctBu (8) and H2AcPh8 (10b) compounds were collected in CCl4 as a solvent.38 In order to clarify such discrepancy, we have collected UV−vis and MCD spectra of the H2NctBu in a large array of solvents (Figure 3). While the spectra of H2NctBu in THF, pyridine, CHCl3, and DCM displayed a single Q-band in the low-energy region, both Qx- and Qy- components were observed in CCl4, heptane, and cyclohexane solutions. Further analysis of the Q-band region suggested that the bandwidth of the single Q-band of H2NctBu which was dissolved in THF, pyridine, and DCM is slightly larger compared with the bandwidths of the Qx- and Qycomponents observed in CCl4 and heptane. Such a difference in the bandwidths is indicative of the small splitting of the Qband into Qx- and Qy-components even in more polar solvents, although the Q-bands remain nonsplit even in benzene, C6F6, or toluene.

3. RESULTS AND DISCUSSION UV−vis and MCD Spectra of Expanded and Peripherally Substituted Pcs and Their Analogues. UV−vis and MCD spectra of investigated metal-free Pcs and their

Figure 3. UV−vis spectra of H2NctBu using a variety of solvents. D


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The Journal of Physical Chemistry A Table 1. Experimental Energies, Splittings, Energy Centers, and Energy Shifts for Q-Bands in 1−11 a

compound H2TAP

tBu

(1)

solvent CCl4 DCM Py

H2PctBu (2)

CCl4 DCM Py

H2(α-OBu)4Pc (3)

THF DCM

H2(α-NEt2)4PctBu (4)

deconv. CCl4d CCl4

H2(α-NBu2)4Pc

CHCl3

H2(α-SPh)4PctBu (5)

THF CCl4

H2(α-SBu)4Pc

THF

H2(α−OHx)8Pc (6)

CCl4

H2(α-OPt)8Pc

PhMe

H2(α-SPhtBu)8Pc (7)

deconv. DCMd DCM

H2(α-SBu)8Pc

THF

H2NctBu (8)

CCl4 heptane DCM Py

H2(α-OBu)8Nc (9)

CCl4 heptane

H2AcPh8 (10)

CCl4

H2ActBu

Py

H2(α-OiPt)8Ac (11)

PhMe

Qy (cm−1)

Qx (cm−1)

λ (nm)

λ (nm)

Qx−Qy (103 cm−1)

0.5[Qx+Qy] (103 cm−1)

Eb (103 cm−1)

refc

18116 552 18083 553 18165 550 15129 661 15106 662 15049 664 14514 689 14454 692 13376 748 13038 767 12987 770 14025 713 14164 706 14085 710 13624 734 13550 738 12449 803 12255 816 12430 805 12987 770 13175 759 12821 780 12762 784 11574 864 11669 857 11062 904 11650 858 10204 980

16051 623 16103 621 16155 619 14286 700 14327 698 14316 698 13850 722 13812 724 12888 776 13038 767 12987 770 13495 741 13550 738 13633 734 13089 764 13123 762 12105 826 12255 816 12430 805 12755 784 12870 777 12821 780 12762 784 11574 864 11669 857 11312 884 11650 858 10482 954

2.065

17.08

0

tw

1.980

17.09

tw

2.010

17.16

30

0.843

14.71

0.779

14.72

tw

0.733

14.68

30

0.664

14.18

0.639

14.13

0.488

13.13

0.000

13.04

tw

0.000

12.99

76

0.529

13.76

0.614

13.86

tw

0.452

13.85

36

0.535

13.36

0.427

13.34

0.344

12.28

0.000

12.26

tw,77

0.000

12.43

36

0.232

12.87

0.305

13.02

tw

0.000

12.82

tw

0.000

12.76

30

0.000

11.57

0.000

11.67

−0.250

11.19

0.000

11.65

−0.278

10.34

−2.37

−2.90

tw,38

tw,36 tw

−3.95

−3.32

−3.72

tw

tw,36

tw 49

−4.80

−4.21

−5.51

tw

tw,36

tw tw

−5.89

38 30

−6.74

39

a Abbreviation: DCM = dichloromethane, Py = pyridine, THF = tetrahydrofuran, PhMe = toluene. bEnergy shift defined as E(0.5[Qx + Qy]) (1) − E(0.5[Qx+Qy]) (x); ctw = this work; ddeconv. = Q-band positions were determined via deconvolution analysis.

E


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Figure 4. Deconvolution spectra of H2(α-NEt2)4PctBu (4) and H2(α-S-p-PhtBu)8Pc (7).

Figure 5. Q-band splitting vs Q-band energy center correlation plots for (a) assumption that 11B2u and 11B3u states do not intercross, (b) the case with a possible 11B2u and 11B3u intercrossing and zero Q-band splitting for compounds 4 and 7, and (c) the case with a possible 11B2u and 11B3u intercrossing and Q-band splitting for compounds 4 and 7 determined by deconvolution analysis.

In order to get additional insight into the aforementioned UV−vis observations, we collected MCD spectra of the H2NctBu in four different solvents. Since all of the metal-free phthalocyanines presented here have no degenerate excited states (as dictated by their effective symmetry) and all of the target compounds are diamagnetic, the MCD spectra of these compounds should be interpreted using MCD Faraday Bterms. Indeed, in the case of MCD spectrum of H2NctBu in CCl4 (when the smallest out of all nonpolar solvents degree of aggregation was observed), the negative and positive MCD Faraday B-terms were clearly observed at 789 and 772 nm, respectively and these signals are closely related to the maxima at 784 and 770 nm observed in the UV−vis spectrum (Figure 2). In the case of more polar solvents, the Q-band maximum observed in the UV−vis spectra roughly corresponds to the MCD signal crossing point, which is typical for MCD Faraday A-terms, which are reflective of the degenerate excited states in porphyrinoids. Taking into consideration an actual effective D2h symmetry of H2NctBu, its MCD spectrum cannot have any Faraday A-terms and the experimentally observed situation can

Figure 6. Typical example of TDDFT-predicted energies and splittings of the Q-band in H2Nc (8a) as a function of used exchange-correlation functional at a single B3LYP/PCM predicted geometry.

Figure 7. Correlation between TDDFT-predicted Q-band center and amount of Hartree−Fock exchange for H2Nc 8a. F


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Table 2. Representative Examples of Computationally Predicted Q-Band Energies, Oscillator Strengths, Splittings, and Energy Centers for All Compoundsa functional/method LC-wPBEb LC-BP86b BP86b TPSShb TPSSh/PCMc B3LYP/PCMd PBE1PBE/PCMd CAM-B3LYP/PCMd ZINDO/Sb

LC-wPBEb LC-BP86b BP86b TPSShb TPSSh/PCMc B3LYP/PCMd PBE1PBE/PCMd CAM-B3LYP/PCMd ZINDO/Sb


Qy (cm−1)

Qx (cm−1)

λ (nm)

λ (nm)

15198 658 14999 667 18191 550 18917 529 18556 539 18407 543 18697 535 17021 588 14214 704

17794 562 17650 567 19137 523 19988 500 19514 512 19444 514 19798 505 18563 539 16821 594

13850 722 13675 731 15616 640 16290 614 15203 658 15270 655 15521 644 14603 685 13566 737

14918 670 14735 679 15873 630 16532 605 15234 656 15202 658 15507 645 14477 691 14489 690

13533 739 13383 747 14498 690 15232 657 14010 714 14316 699 14601 685 13994 715 13399 746

14534 688 14384 695 14113 709 15503 645 13857 722 14137 707 14454 692 13851 722 14298 699

f (Qy)e

f (Qx)e

Qx−Qy (103 cm−1)

0.5[Qx+Qy] (103 cm−1)

H2TAP (1a) 0.1735

0.1678

2.596

16.50

0.1893

0.1825

2.651

16.32

0.0537

0.0562

0.946

18.66

0.0951

0.0959

1.071

19.45

0.2910

0.3039

0.958

19.04

0.3396

0.3504

1.037

18.93

0.3781

0.3830

1.101

19.25

0.3979

0.4011

1.542

17.79

0.2769

0.3100

1.598

15.52

H2Pc (2a) 0.4304

0.5018

1.068

14.38

0.4533

0.5218

1.060

14.21

0.2779

0.3350

0.257

15.74

0.3477

0.4003

0.242

16.41

0.7928

0.7517

0.031

15.22

0.7935

0.8307

−0.068

15.24

0.8352

0.8653

−0.014

15.51

0.8838

0.8347

−0.126

14.54

0.6445

0.8279

0.923

14.03

H2(α-OMe)4Pc (3a) 0.4790 0.5583

1.001

14.03

0.5013

0.5771

1.001

13.88

0.3545

0.2613

−0.385

14.31

0.3671

0.4394

0.271

15.37

0.7871

0.8048

−0.152

13.93

0.8467

0.8706

−0.179

14.23

0.8997

0.9067

−0.147

14.53

0.9486

0.9202

−0.143

13.92

0.6791

0.8661

0.899

13.85

G


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The Journal of Physical Chemistry A Table 2. continued functional/method LC-wPBEb LC-BP86b BP86b TPSShb TPSSh/PCMc B3LYP/PCMd PBE1PBE/PCMd CAM-B3LYP/PCMd ZINDO/Sb



Qy (cm−1)

Qx (cm−1)

λ (nm)

λ (nm)

13056 766 12888 776 12124 825 13835 723 12559 796 13323 751 13601 735 13468 743 13286 753

13947 717 13779 726 11378 879 13438 744 12352 810 13079 765 13402 746 13342 750 14115 708

13458 743 13299 752 13326 750 14583 686 13625 734 14034 713 14323 698 13919 718 13528 739

14403 694 14242 702 12825 780 14811 675 13456 743 13831 723 14172 706 13859 722 14416 694

13193 758 13087 764 12743 785 13899 719 12390 807 13045 767 13329 750 13176 759 13207 757

14100 709 14001 714 12303 813 14126 708 12248 816 12823 780 13153 760 13113 763 14076 710

f (Qy)e

f (Qx)e

H2(α-NMe2)4Pc (4a) 0.5072 0.5792

Qx−Qy (103 cm−1)

0.5[Qx+Qy] (103 cm−1)

0.891

13.50

0.5258

0.5914

0.891

13.33

0.2399

0.1104

−0.746

11.75

0.3853

0.2770

−0.397

13.64

0.6681

0.7012

−0.207

12.46

0.7902

0.8260

−0.244

13.20

0.8530

0.8775

−0.199

13.51

0.9541

0.9415

−0.126

13.41

0.7022

0.8845

0.829

13.70

H2(α-SMe)4Pc (5a) 0.4793 0.5587

0.945

13.93

0.5025

0.5783

0.943

13.77

0.3011

0.1608

−0.501

13.08

0.3213

0.4183

0.228

14.70

0.7400

0.7886

−0.169

13.54

0.8301

0.8703

−0.203

13.93

0.8832

0.9125

−0.151

14.25

0.9615

0.9298

−0.060

13.89

0.6657

0.8504

0.888

13.97

H2(α-OMe)8Pc (6a) 0.5233 0.6109

0.907

13.65

0.5439

0.6280

0.914

13.54

0.3022

0.1943

−0.440

12.52

0.3339

0.4313

0.227

14.01

0.7182

0.8013

−0.143

12.32

0.8386

0.8964

−0.222

12.93

0.9003

0.9470

−0.176

13.24

0.9881

1.0365

−0.063

13.14

0.7123

0.9111

0.869

13.64

H


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Qy (cm−1)

Qx (cm−1)

λ (nm)

λ (nm)

12492 801 12357 809 10960 912 12591 794 11698 855 12347 810 12577 795 12644 791 13124 762

13279 753 13154 760 10482 954 12754 784 11496 870 12071 828 12353 809 12580 795 13916 719

12773 783 12607 793 13052 766 13978 715 12778 783 13045 767 13314 751 12803 781 13000 769

12929 773 12726 786 12602 794 13482 742 12109 826 12298 813 12620 792 12161 822 12960 772

11669 857 11542 866 11171 895 12253 816 11430 875 11992 834 12188 820 11927 838 12362 809

11596 862 11437 874 10836 923 11813 846 10761 929 11209 892 11458 873 11183 894 12298 813

f (Qy)e

f (Qx)e

H2(α-SMe)8Pc (7a; C2v) 0.4800 0.5469

Qx−Qy (103 cm−1)

0.5[Qx+Qy] (103 cm−1)

0.787

12.89

0.5012

0.5653

0.797

12.76

0.1940

0.0943

−0.478

10.72

0.2443

0.3494

0.163

12.67

0.6317

0.6983

−0.202

11.60

0.7614

0.7957

−0.276

12.21

0.8169

0.8445

−0.224

12.47

0.9049

0.9363

−0.064

12.61

0.6589

0.8293

0.792

13.52

H2Nc (8a) 0.6769

0.7642

0.156

12.85

0.7052

0.7870

0.119

12.67

0.3897

0.4300

−0.450

12.83

0.5135

0.5442

−0.496

13.73

1.0043

0.9898

−0.669

12.44

1.0760

1.0517

−0.747

12.67

1.1304

1.1009

−0.694

12.97

1.1616

1.1716

−0.642

12.48

1.1595

0.9453

−0.040

12.98

H2(α-OMe)8Nc (9a) 0.7436 0.7944

−0.073

11.63

0.7719

0.8163

−0.105

11.49

0.3413

0.3875

−0.335

11.00

0.4819

0.5107

−0.440

12.03

0.9804

0.9647

−0.669

11.10

1.0796

1.0509

−0.783

11.60

1.1414

1.1052

−0.730

11.82

1.2171

1.2089

−0.744

11.56

1.2716

1.0600

−0.064

12.33

I


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Qy (cm−1)

Qx (cm−1)

λ (nm)

λ (nm)

12075 828 11908 840 10915 916 12121 825 11031 906 11521 868 11830 845 11784 849 12724 786

11694 855 11473 872 9679 1033 10912 916 9895 1011 10307 970 10673 937 10688 936 12187 821

10965 912 10835 923 9742 1027 10872 920 10014 999 10679 936 10884 919 10939 914 12198 820

10406 961 10230 978 8811 1135 9912 1009 8968 1115 9501 1053 9763 1024 9784 1022 11659 858

f (Qy)e

f (Qx)e

Qx−Qy (103 cm−1)

0.5[Qx+Qy] (103 cm−1)

H2Ac (10a) 0.8959

0.9677

−0.381

11.89

0.9284

0.9915

−0.435

11.69

0.3519

0.3102

−1.236

10.30

0.4731

0.5364

−1.209

11.52

1.0825

0.9789

−1.135

10.46

1.2140

1.0962

−1.214

10.91

1.2904

1.1679

−1.157

11.25

1.4006

1.3469

−1.096

11.24

1.1525

1.2818

−0.537

12.46

H2(α-OMe)8Ac (11a) 0.9626 0.9819

−0.559

10.68

0.9955

1.0056

−0.605

10.53

0.3636

0.3365

−0.931

9.28

0.5405

0.4941

−0.960

10.39

1.0802

0.9724

−1.046

9.49

1.2230

1.1019

−1.178

10.09

1.3038

1.1749

−1.121

10.32

1.4494

1.3731

−1.155

10.36

1.8583

1.4980

−0.539

11.93

a Selected data for several geometries and exchange-correlation functionals. bBP86 gas phase geometry. cTPSSh/PCM geometry; dB3LYP/PCM geometry. eTDDFT-predicted oscillator strengths

Table 3. Representative Examples of Regression Analysis Data for the Q-Bands Energy Center (Figure 8) exchangecorrelation functional

LC-wPBEa

LC-BP86a

BP86a

TPSSha

TPSSh/PCMb

B3LYP/PCMc

PBE1PBE/PCMc

CAM-B3LYP/PCMc

ZINDO/Sa

intercept slope R R2 MAD (cm−1)

−2.4122 1.17182 0.98857 0.97727 329

−2.2014 1.3242 0.98058 0.96153 348

4.59053 0.67033 0.97415 0.94897 887

2.81913 0.73713 0.99653 0.99308 859

4.10005 0.70182 0.98436 0.96896 709

2.97112 0.76598 0.98869 0.97751 357

2.80813 0.76167 0.98953 0.97916 448

0.94958 0.92469 0.98883 0.97778 234

−11.0702 1.79978 0.96622 0.93358 782

a

BP86 gas phase geometry. bTPSSh/PCM geometry. cB3LYP/PCM geometry.

of H-aggregates, typical for Pcs and their analogues, results in the appearance of new, blue-shifted broad bands, which are associated with a negative to positive pattern in their MCD spectra.75 Thus, the ratio of MCD intensities of the positive component of the Q-band in H2NctBu and the negative component in MCD spectra located at ∼821 nm was used to confirm the relative degree of aggregation of this compound in

be reflective of accidental degeneracy, which already has been discussed numerous times.28,29,38,39 Such accidental degeneracy results in the observation of a MCD Faraday pseudo Aterm, which actually consists of two closely spaced MCD Faraday B-terms of opposite signs. Another clear trend observed in the MCD spectra of H2NctBu in different solvents is the aggregation behavior. It is well-known that the formation J


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The Journal of Physical Chemistry A Table 4. Representative Examples of Regression Analysis Data for the Q-Band Splitting (Figure 9) exchangecorrelation functional

LC-wPBEa

LC-BP86a

BP86a

TPSSha

TPSSh/PCMb

B3LYP/PCMc

PBE1PBE/PCMc

CAM-B3LYP/PCMc

ZINDO/Sa

intercept slope R R2 MAD (cm−1)

−0.0083 0.71723 0.97667 0.95389 299

0.01338 0.68985 0.97265 0.94605 325

0.8618 1.00064 0.90703 0.82271 862

0.57523 0.88887 0.90348 0.81627 558

0.80648 1.08706 0.97512 0.95086 780

0.84465 1.01035 0.98028 0.96094 841

0.79284 1.01061 0.98134 0.96303 789

0.67895 0.85785 0.9745 0.94965 714

0.0489 0.69927 0.97107 0.94297 293

a


Table 5. Representative Examples Regression Analysis Data for Individual Qx and Qy Intercepts (Figure 10) exchange-correlation functional

LCwPBEa

LCBP86a

BP86a

TPSSha

TPSSh/ PCMb

B3LYP/ PCMc

PBE1PBE/ PCMc

CAM-B3LYP/ PCMc

ZINDO/ Sa

Qx intercept slope R R2 MAD (cm−1) Qy intercept slope R R2 MAD (cm−1)

1478 0.90675 0.98753 0.97522 338 3492 0.73192 0.98845 0.97704 333

1340 0.90495 0.98149 0.96333 347 3610 0.71192 0.98287 0.96603 399

−5213 1.32858 0.97184 0.94446 1141 −6897 1.53788 0.97591 0.9524 762

−3277 1.28735 0.99718 0.99438 645 −4365 1.42779 0.99117 0.98242 1153

−4807 1.31079 0.9898 0.97971 925 −5992 1.47445 0.97532 0.95124 551

−3388 1.23196 0.99266 0.98538 542 −3732 1.33223 0.98164 0.96361 562

−3185 1.2402 0.99313 0.9863 379 −3626 1.34436 0.98287 0.96604 816

−1186 1.06523 0.98861 0.97736 420 −216 1.04772 0.98826 0.97666 399

5211 0.63858 0.96599 0.93313 776 8582 0.35388 0.9581 0.91796 794

a


(2). The Q-bands center in the H2(α-OC6H13)8Pc (6), H2(αOBu)8Nc (9), and H2(α-OiPent)8Ac (11) sequence is ∼100 nm red-shifted upon stepwise benzannulation of the parent aromatic core. The Qx- and Qy-bands in H2(α-OBu)8Nc (9), H2(α-p-SPhtBu)8Pc (7), and H2(α-NMe)4PctBu (4) are collapsed into a single, broad band with corresponding Faraday pseudo A-terms observed in their MCD spectra. The H2(α-NEt2)4PctBu system has the broadest Q-band (FWHW ∼1200 cm−1). Because of such a large Q-band broadening in the H2(α-NEt2)4PctBu compound, we have analyzed the FWHW values for all other compounds presented in this paper. The single Q-bands of the H2(α-NEt2)4PctBu (∼1200 cm−1) and H2(α-S-p-PhtBu)8Pc (∼820 cm−1) compounds have the largest magnitude of unusual broadening when compared to the other compounds (∼300−500 cm−1). Q-band broadening in similar compounds was previously observed,31,77 but not discussed in detail. It can either reflect the overlap of two close-energy Qx- and Qy-bands or the presence of several positional isomers (H2(α-NEt2)4PctBu only). As recently shown by Jiang,76 Kobayashi,36 and us,78 because of the relative bulkiness of the NR2 groups in H2(αNR2)4Pcs and their metal complexes, the formation of the most symmetric phthalocyanines (Figure 1) is preferred, and thus, one can assume that the UV−vis and MCD spectra of H2(α-NEt2)4PctBu are dominated by a single positional isomer. Moreover, the positional isomers argument is not applicable to a symmetric H2(α-S-p-PhtBu)8Pc (7) that still has an unusually broad (FWHW ∼820 cm−1) Q-band. Therefore, proposing that the single, anomalously broad Q-band of the H2(αNEt2)4PctBu (4) and H2(α-S-p-PhtBu)8Pc (7) compounds is indicative of the closely spaced Qx- and Qy-bands, we conducted a band deconvolution analysis on the Q-band region (Figure 4). Although the band deconvolution analysis converged to similar results from different starting points, the Qx- and Qyband energies (Table 1) have a large degree of uncertainty and

different solvents. Following this criterion, the degree of aggregation increases in the following order: Py < THF < CCl4 < DCM. Overall, although not surprising, π−π* transitions in the Q-band region showed a small solvatochromic effect, which nevertheless results in several cases of the Q-band splitting into Qx- and Qy-components and also leads to solvent-dependent aggregation of H2NctBu. Similarly, to H2NctBu, the Qx- and Qyband splitting in H2TAPtBu and H2PctBu is also slightly solvatochromic and reaches ∼100 cm−1, in the case of the most studied H2PctBu compound (Table 1). Again, the largest splitting observed in the UV−vis and MCD spectra of H2TAPtBu and H2PctBu was observed with nonpolar solvents such as CCl4. Available data on H2Ac(R)n compounds are also in agreement with the solvent polarity dependence. Indeed, the UV−vis spectrum of octaphenylsubstituted H2AcPh8 (10b) in CCl4 has individual Qx- and Qybands separated by ∼250 cm−1,38 while the UV−vis spectrum of tetra-tert-butyl substituted H2ActBu, recorded in the more polar pyridine solvent, has only a single Q-band which is associated with an MCD Faraday pseudo A-term (Table 1).30 In the case of H2NcR(n) and H2AcR(n) compounds, additional bands in their UV−vis and MCD spectra were also observed in the 450−600 nm region (Figure 2). Taking into consideration the better resolution of the Qxand Qy- bands in nonpolar solvents, we also investigated the UV−vis and MCD spectra of α-substituted by electrondonating groups Pcs and Ncs in CCl4. Although the use of CCl4 allowed us to clearly resolve the Qx- and Qy-components of the Q-band in the H2(α-OC6H13)8Pc compound 6, the general trends for alkoxy- and arylthiol-substituted compounds agree well with the previously reported data collected on similar compounds in more polar THF by Kobayashi, Lukyanets, and co-workers.36 For the same number of substituents, the Q-band shift increases in the following order: -OR < -SR < -NR2 with H2(α-NEt2)4PctBu (4) having ∼100 nm red-shifted Q-band compared to the parent H2PctBu K


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Figure 8. MAD analysis for array of 330 excited state calculations for BP86 gas phase, BP86/PCM, B3LYP gas phase, and B3LYP/PCM geometries.

experimental observation that the Qx − Qy-band splitting in H2NctBu < H2AcPh8 and H2(α-OBu)8Nc < H2(α-OiPent)8Ac pairs increases with the increase of the aromatic π-system contradicts the earlier suggestion that the Qx- and Qy- bands in metal-free phthalocyanines and their analogues collapse into a single band when the target compounds have absorption above ∼770 nm. Indeed, if one would assume a lack of the 11B2u and 11B3u intercrossing, then the energy center of the Q-bands versus QxQy splitting graph will have a “J-shape” character (Figure 5a). If it is assumed that the intercrossing between the 11B2u and 11B3u excited states is possible, then the 0.5(Qx+Qy)/(Qx-Qy) correlation graph becomes more linear with the H2(αNEt2)4PctBu (4) and H2(α-S-p-PhtBu)8Pc (7) compounds being the largest outliers (Figure 5b). Finally, if we use band deconvolution results to resolve anomalous broadening of the Q-band in the H2(α-NEt2)4PctBu and H2(α-S-p-PhtBu)8Pc compounds, then the center of energy 0.5(Qx+Qy) correlation would be the most straightforward (Figure 5c). TDDFT and ZINDO/S Calculations on Selected MetalFree Phthalocyanines and Their Analogues. In order to

should be treated with caution. Nevertheless, the band deconvolution energies and splittings provide a good explanation of the anomalous broadening of the single Qband in the H2(α-NEt2)4PctBu (4) and H2(α-S-p-PhtBu)8Pc (7) compounds and fits better into the experimental 0.5(Qx + Qy)/ (Qx-Qy) correlation discussed below. H2(α-OC6H13)8Pc (6), H 2 (α-SPh) 4 Pc tBu (5), H 2 (α-p-SPh tBu ) 8 Pc (7), H 2 (αNMe2)4PctBu (4), H2(α-OBu)8Nc (9), and H2(α-OiPent)8Ac (11) compounds have additional absorption bands in the 450−600 nm region that were assigned to the interligand -OR/-SR/-NR2 to -Pc/Nc/Ac charge-transfer (ICT) transitions32 and will be discussed below in conjunction with TDDFT calculations. In the case of alkoxy-derivatives, the Qx − Qy bands splitting follows the following order: H2(αOBu)4Pc > H2(α-OC6H13)8Pc > H2(α-OBu)8Nc < H2(αOiPent)8Ac. Similarly, in the parent systems in CCl4, the Qxand Qy-splitting follows the order: H2TAPtBu (1) > H2PctBu (2) > H2NctBu (8) < H2AcPh8 (10b). Both of these trends are potentially indicative of crossover behavior of the 11B2u and 11B 3u (in D2h symmetry notation) excited states. An L


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Figure 9. Representative examples for linear correlations for the experimental vs calculated energies of Q-bands center for all compounds. Blue line represents ideal correlation.

clarify the proposed potential intercrossing between 11B2u and 11B3u states in the metal-free phthalocyanines and their analogues, we used time-dependent density functional theory (TDDFT) and semiempirical ZINDO/S calculations on all compounds listed in Figure 1 Supporting Information Figures S1−S55). There are several theoretical studies on coreextended, metal-free tetraazaporphyrins that are available in the literature.30,31,79 For instance, Kobayashi and co-workers used semiempirical ZINDO/S calculations to explore spectroscopic trends in expanded metal-free tetraazaporphyrins.30 Several TDDFT-based reports on metal-free phthalocyanine and its analogues are also available in the literature.45,46 In two interesting papers, Nakatsuji and co-workers31,47 compared SAC−CI methodology with TDDFT results on the metal-free tetraazaporphyrin and its expanded analogues. The electronic structures and the vertical excitation energies of several −OR and −SR α-substituted phthalocyanines predicted on the basis of B3LYP TDDFT calculations were discussed by Zhang, Kobayashi, Stillman, and co-workers.34,80 TDDFT calculations on several specific, α-substituted with − NR2 groups phthalocyanines are also available.36,76,78 To the best of our knowledge, however, there is no systematic investigation of influence of the exchange-correlation functionals on the predicted vertical excitation energies in both expanded metalfree tetraazaporphyrins and substituted with a large variety of electron-donating groups phthalocyanines and their analogues available in literature. Although it was proven before that the

TDDFT approach could be successfully used for the investigation of the electronic structures and origins of the vertical excitation energies in porphyrinoids,81,82 it has also been shown that an amount of the Hartree−Fock exchange presented in the exchange-correlation functional is more important for the calculation of the energies of π−π* and nπ* transitions in phthalocyanines than the quality of the basis sets83 (assuming that the minimal basis set would be of doubleζ quality and includes a polarization function on heavy atoms). Since we were initially interested in an accurate prediction of the Qx- and Qy-band energies as well as Qx/Qy-band splitting in the metal-free Pcs and their analogues, we used H2Nc (8a) as a test compound to confirm a dominant influence of the nature of the exchange-correlation functionals on the mentioned above properties (Figure 6 and S56). In order to study the influence of the starting geometry on the TDDFT-predicted energies of the Q-bands, we also tested a large number of the exchange-correlation functionals for BP86 and B3LYP-predicted geometries of H2Nc (8a, Figures 6 and S56). In agreement with the previous calculations on Pcs and their analogues, we found that the amount of the Hartree− Fock exchange present in the exchange-correlation functional correlates well with the calculated vertical excitation energies of the Qx- and Qy-bands and their splitting (Figure 7). In general, GGA and long-range corrected GGA related exchange-correlation functionals (i.e., BP86, LC-BP86, and LC-wPBE) provide a better agreement between theory and M


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Figure 10. Representative examples of correlations between experimental vs calculated Q-band splittings for all compounds. Blue line represents ideal correlation.

experiment compared with the “hybrid” exchange-correlation functionals. For instance, in the case of the more popular B3LYP exchange-correlation functional (∼20% of Hartree− Fock exchange), the Qx- and Qy-band energies are overestimated by ∼0.2 eV, and this error increases with the amount of Hartree−Fock exchange present in the exchange-correlation functional. The influence of the initial geometry on the TDDFT-predicted vertical excitation energies was found to be rather minor. Based on the “calibration” TDDFT calculations, and in order to cover a broad range of the exchangecorrelations functionals, we used BP86 (pure GGA), LC-BP86 (long-range corrected GGA), LC-wPBE (long-range corrected GGA), TPSSh (hybrid meta-GGA with lower amount of Hartree−Fock exchange), B3LYP (standard hybrid), CAMB3LYP (long-range corrected hybrid), and PBE1PBE (hybrid with higher amount of Hartree−Fock exchange) exchangecorrelation functionals for all compounds of interest. In addition, we also used a semiempirical ZINDO/S59 method as a reference because it was a traditional choice for calculation of the vertical excitation energies of Pcs and their analogues for a long time30 and it was interesting for us to see its performance compared with the more expensive TDDFT approach. In order to rectify an exchange-correlation dependent variation on calculated geometries and vertical excitation energies and compare calculations in the gas phase and solution, we have run a complete array of calculations for four DFT-optimized geometries (BP86 in gas phase snd solution as well as B3LYP in a gas phase and solution) and seven

exchange-correlation functionals (BP86, LC-BP86, LC-wPBE, TPSSh, B3LYP, PBE1PBE, and CAM-B3LYP) for compounds 1−11 (total of 308 TDDFT calculations). In addition, we run ZINDO/S calculations for compounds 1−11 for BP86 and B3LYP gas-phase geometries. Finally, to better explore exchange-correlation dependency on the TDDFT-predicted properties of compounds 1−11, we compared four additional pairs: BP86/PCM geometry−BP86/PCM TDDFT, TPSSh/ PCM geometry−TPSSh/PCM TDDFT, B3LYP/PCM geometry B3LYP/PCM TDDFT, and PBE1PBE/PCM geometry− PBE1PBE/PCM TDDFT. The overall results for these 352 calculations are summarized in Tables 2−5 , Supporting Information Table S1, Figures 8−12 and Figures S1−S56 with detailed discussion on the data provided in the section below. General Trends in Predicted Energies of Q-Bands. In order to estimate the TDDFT or ZINDO/S predicted trends in the energies of Q-bands, we have plotted the experimentally observed center of the Q-bands versus the theoretically predicted values (calculated as E = 0.5(Qx+Qy) in cm−1 scale, Figures 8 and 9). Numerical linear regression analysis data are shown in Supporting Information Table 3 and Table S1. Numerical analysis of the data (Figures 8 and 9, Table S1) indicates that the closest to unity slopes and smallest intercepts were achieved for the LC-wPBE, LC-BP86 (both for BP86 gas phase geometry), and CAM-B3LYP/PCM (B3LYP/PCM geometry) exchange-correlation functionals. LC-wPBE, LCBP86 (both for BP86 gas phase geometry), as well as B3LYP/ PCM, and CAM-B3LYP/PCM (both for B3LYP/PCM N


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Figure 11. Representative examples of TDDFT-predicted vs experimental Qx- and Qy-band energy correlations for all compounds.

traditional D2h notation) do not intercross and the Qx- and Qybands in compounds 4 and 7 do not split. From the data, it is clear to see that the LC-wPBE and LC-BP86 exchangecorrelation functionals as well as semiempirical ZINDO/S provide a correct H2TAP > H2Pc > H2Nc ∼ 0 < H2Ac relationship for the set of parent macrocycles and predict splitting between Qx- and Qy-bands within 0.05 eV accuracy as compared to the experimental data independently of the group. Interestingly, the correlation line slope for BP86, TPSSh/ PCM, B3LYP/PCM, and PBE1PBE/PCM approaches is close to unity, although the TDDFT-predicted MADs are significantly higher than for the LC-wPBE and LC-BP86 exchange correlation functionals (Figure 10). More detailed analysis on the TDDFT and ZINDO/S predicted values for the energies of the Qx- and Qy-bands is given in Figure 11 and Tables 5 and S1. Following Nakatsuji31 and Kobayashi,36 we defined the Qxband as the transition that is dominated by a single-electron excitation from “a1u” occupied orbital in D4h notation (the HOMO in all cases) to one of the “eg” orbitals (the LUMO or LUMO+1 orbital that has no electron density at the nitrogen atoms of N−H (Figure 13) and Qy-band as the transition that is dominated by a single-electron excitation from the “a1u” occupied orbital in D4h notation (the HOMO in all cases) to one of the “eg” orbitals (the LUMO or LUMO+1 orbital that has electron density at the nitrogen atoms of N−H). Our TDDFT and ZINDO/S calculations are indicative that the only LC-wPBE and LC-BP86 predicted energies of Qx- and Qy-bands correlate well (within 0.05 eV MAD) with the

geometry) exchange-correlation functionals were the only functionals that provided better than 0.05 eV (∼400 cm−1) accuracy for the center energies of the Q-bands of the compounds of interest (Figure 8). General Trends in Predicted Splitting of Q-Bands. TDDFT and ZINDO/S predicted splitting between the Qxand Qy-bands versus experimental data is graphically shown in Figures 8 and 10 with numerical regression analysis values listed in Table 4 and Table S1. In order to avoid any unambiguous results on the TDDFT-predicted Qx/Qy-bands splitting, we have grouped TDDFT/ZINDO/S results into four different categories (Figure 8). The group “1” (Figure 8) represents the MAD values for TDDFT or ZINDO/S Qx/Qybands splitting assuming that the 11B2u and 11B3u states (in traditional D2h notation) are intercrossing and the Qx- and Qybands in compounds 4 and 7 split as shown by band deconvolution analysis (Figure 4). The group “2” (Figure 8) represents the MAD values for TDDFT or ZINDO/S Qx/Qybands splitting assuming that the 11B2u and 11B3u states (in traditional D2h notation) intercross but the Qx- and Qy-bands in compounds 4 and 7 do not split. The group “3” (Figure 8) represents the MAD values for TDDFT or ZINDO/S Qx/Qybands splitting assuming that the 11B2u and 11B3u states (in traditional D2h notation) do not intercross and the Qx- and Qybands in compounds 4 and 7 split as shown by band deconvolution analysis (Figure 4). The group “4” (Figure 8) represents the MAD values for TDDFT or ZINDO/S Qx/Qybands splitting assuming that the 11B2u and 11B3u states (in O


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Figure 12. Representative examples of correlation diagrams of the calculated energies of the Qx- or Qy-bands vs Q-band energy center for all compounds.

such intercrossing at the energies close to the H2Nc (8a) system, which agree well with the available experimental data. Overall, our data suggests that when the accurate (0.05 eV or better) prediction of the Qx- and Qy-band energies in the metal-free phthalocyanines and their analogues is required, the long-range corrected LC-wPBE and LC-BP86 methods provide the best agreement between theory and experiment. Description of Transitions in the 450−600 nm Region Observed for Alkoxy-, Aryl Sulfanyl-, and AminoGroup-Containing Systems. It is well-established that the phthalocyanines substituted at the α-positions with electrondonating -OR, -SR, and -NR2 groups have low-intensity broad absorption profiles between the Q- and B-band regions that were attributed to transitions with predominant substituent-tomacrocycle interligand charge-transfer character.34,36,49,76,80 Since we already had a large array of TDDFT and ZINDO/ S calculations, it was interesting to see if LC-wPBE and LCBP86 methods that are superior in the prediction of Q-band region would work equally well for the prediction of this ICT region (Figure 14 and Figures S1−S55). The analysis of our TDDFT data, however, clearly shows that the energies of such charge-transfer transitions are clearly overestimated by these two exchange-correlation functionals as no transitions were predicted between the Q- and B-band regions (Figure 14 and S1−S55). Such an observation is not entirely surprising as both exchange-correlation functionals have 100% of Hartree−Fock exchange included for the long-range transitions such as ICT,

experimental data. In addition, PBE1PBE/PCM and CAMB3LYP/PCM (both for B3LYP/PCM geometry) methods agree well with the energies of the Qx- or Qy-bands, respectively but not for both (Table 5 and S1). Available experimental data for the metal-free phthalocyanines are suggestive of the monotonic decrease of the energy splitting between the Qx- and Qy-bands of H2TAP and H2Nc. However, an experimentally observed increase of the energy splitting between the Qx- and Qy-bands in H2NctBu < H2AcPh8 and H2(α-Bu)8Nc < H2(α-OiPent)8Ac can only be explained if one would assume a possibility of an intercrossing of the 11B2u and 11B3u excited states in the metal-free phthalocyanines and their analogues. Such intercrossing between these excited states was reported earlier for both TDDFT and ZINDO/S calculations30,45,46 and contrasted with the SAC−CI predictions.31,47 From Figure 12, it is clear that all TDDFT methods and the ZINDO/S approach predicted intercrossing of the 11B2u and 11B3u excited states in the metal-free phthalocyanines and their analogues, which agrees well with all the previous sporadic calculations on the similar systems.34,36,37,79,80 The energy of such intercrossing has a prominent dependency on the specific exchange-correlation functional. Indeed, TPSSh, B3LYP, PBE1PBE, and CAM-B3LYP methods (for all geometries tested in the gas phase and solution) predict such intercrossing close to the Q-band energy in H2Pc (2a), which disagrees with the experimental data (Figures 2 and 5). The LC-wPBE and LC-BP86 exchange-correlation functionals (for all geometries tested both in a gas phase and solution) predict P


Article


Figure 13. Representative examples of the frontier molecular orbitals of all compounds.

Figure 14. Typical comparison for experimental (top row) and calculated UV−vis spectra for compound 4. Vertical red bars represent predicted energies and intensities of Qx- and Qy-bands. For the other individual graphs, see Supporting Information Figures S1−S55.

compounds of interest (Figure 14), which also leads to heavy mixing of the charge-transfer and macrocycle-based π−π* transitions in the Q-band region. Although π−π* and charge-

which clearly leads to their overestimated energies. The pure GGA BP86 exchange-correlation functional clearly underestimates the energies of the charge-transfer transitions in the Q


Article


TDDFT (10% of Hartree−Fock exchange), B3LYP/PCM geometry−B3LYP/PCM TDDFT (20% of Hartree−Fock exchange), PBE1PBE/PCM geometry−PBE1PBE/PCM TDDFT (25% of Hartree−Fock exchange) pairs in solution (Figure 15 and Supporting Information Figures S44−S55). In all cases, the monotonic increase of the TDDFT-predicted energy center for Qx/Qy-bands and ICT bands was observed, which suggest that the energies of both π−π* and ICT transitions monotonically increase with the amount of Hatree− Fock exchange in the exchange-correlation functional. Overall, our TDDFT data suggest that some of the standard exchange-corelation functionals can either predict correct energies and splittings of Qx- and Qy-bands in metal-free phthalocyanines and their analogues or correct energies of the ICT bands in the same systems with a great accuracy (MAD < 0.05 eV) but not both. One of the possible approach to improve global agreement between theory and experiment in compounds 1−11 might be use of the first-principles LC tuning methodology,84,85 and we are currently exploring this idea.

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CONCLUSIONS

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ASSOCIATED CONTENT

An insight into the electronic structure of unsubstituted and nonperipherally substituted with electron-donating groups metal-free H2TAPs, H2Pcs, H2Ncs, and H2Acs with a focus on Q-band energies and their splitting has been gained and discussed on the basis of experimental UV−vis and MCD data as well as DFT, TDDFT, and semiempirical ZINDO/S calculations. Experimental data are suggestive of intercrossing between the “11B2u” and “11B3u” excited states around 800 nm spectral region. A large array of exchange-correlation functionals were tested for the prediction of vertical excitation energies in H2TAPs, H2Pcs, H2Ncs, and H2Acs. In general, the TDDFT-predicted energies of the Qx- and Qy-bands and their splitting correlate well with the amount of Hartree−Fock exchange present in the specific exchange-correlation functional with the LC-BP86 and LC-wPBE ECFs providing the best agreement between theory and experiment (

Simultaneous Prediction of the Energies of Qx and Qy Bands and

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