DFT Studies of Dimethylaminophenyl-Substituted Phthalocyanine and Its Silver Complexes

The dimethylaminophenyl-substituted silver phthalocyanine [dmaphPcAg] can be used as a UV-vis photoinitiator for in situ preparation of a silver/polymer nanocomposite. To verify early steps of the supposed mechanism of radical polymerization, we performed quantum chemical calculations of m[dmaphPcAg]q complexes with charges q = +1 to −2 in the two lowest spin states m, of a free ligand and its dehydrogenated/deprotonated products m[dmaphPcHn]q, n = 2 to 0, q = 0, −1 or −2, in the lowest spin states m. The calculated electronic structures and electron transitions of all the optimized structures in CHCl3 solutions are compared with experimental EPR and UV-vis spectra, respectively. The unstable 3[dmaphPcAg]+ species deduced only from previous EPR spin trap experiments was identified. In addition to 2[dmaphPcAg]0, our results suggest the coexistence of both reaction intermediates 1[dmaphPcAg]− and 3[dmaphPcAg]− in reaction solutions. Silver nanoparticle formation is a weak point of the supposed reaction mechanism from the energetic, stereochemistry, and electronic structure points of view.

Very high absorption in the visible range and high chemical resistance implied the synthesis of complexes of various substituted phthalocyanines with central Al, Mg, and Zn atoms [18][19][20][21][22] to be used as photoinitiators for free-radical (FRP) and/or cationic (CP) polymerizations.Recently, Breloy et al. [23] have synthesized a complex of dimethylaminophenylsubstituted phthalocyanine with silver in an unusual oxidation state +II, 2 [dmaphPcAg] 0 (see Figure 1.In the used notation, left superscripts denote spin multiplicities m = 2S +1, where S is the total spin angular momentum.The right superscripts denote charges).The species obtained by photoinduced electron transfer reactions of excited m [dmaphPcAg] 0 * initiated FRP both in laminate as well as in the air.Moreover, a polymer/silver nanocomposite with a homogenous narrow size distribution of spherical silver nanoparticles was formed.Under exposure to LED@385 nm of 2 [dmaphPcAg] 0 in CHCl3 solutions a sharp decrease in absorbance at 359 and 723 nm is observed simultaneously with splitting of the Q-band and a rapid increase in a band at 450 nm indicating the formation of silver nanoparticles (see Figure S2 in Supplementary Information) [23].Well-dispersed spherical Ag nanoparticles in the solution (an average diameter of 9 nm) were confirmed by transmission electron microscopy.
A very weak EPR signal of in situ irradiated 2 [dmaphPcAg] 0 in CHCl3 using LED@385 nm was detected at g = 2.0021 [23].It can be assigned to an unstable π-radical cation which is probably transformed into an N-centered radical that was detected as an adduct with N-benzylidene-tert-butylamine N-oxide (PBN) or 2,2-dimethyl-3,4-dihydro-2H-pyrrole 1oxide (DMPO).The carbon-and nitrogen-centered radicals were detected in similar EPR experiments with PBN and DMPO spin-traps in deoxygenated benzene under argon as well [23].
Because radical species are strongly inhibited by oxygen, FRP does not proceed well in air.Unlike acrylate conversions, epoxy conversions are not affected by atmospheric conditions.Another interesting attribute of the above 2 [dmaphPcAg] 0 photoinitiating systems is the electron transfer reactions where the central Ag(II) atom is reduced to homogenously dispersed silver nanoparticles in the polymer matrix.
The following 2 [dmaphPcAg] 0 photoinitiation mechanism was proposed [23]: The photoexcited [dmaphPcAg]* is formed via irradiation in the first step 2 The reaction between photoexcited and ground-state species leads to the reduction of Ag(II) to Ag(I) and generates the nitrogen-centered cation radical in the second step In the third step, silver nanoparticles and aromatic carbon-centered radicals are formed.Under exposure to LED@385 nm of 2 [dmaphPcAg] 0 in CHCl 3 solutions a sharp decrease in absorbance at 359 and 723 nm is observed simultaneously with splitting of the Q-band and a rapid increase in a band at 450 nm indicating the formation of silver nanoparticles (see Figure S2 in Supplementary Information) [23].Well-dispersed spherical Ag nanoparticles in the solution (an average diameter of 9 nm) were confirmed by transmission electron microscopy.
Because radical species are strongly inhibited by oxygen, FRP does not proceed well in air.Unlike acrylate conversions, epoxy conversions are not affected by atmospheric conditions.Another interesting attribute of the above 2 [dmaphPcAg] 0 photoinitiating systems is the electron transfer reactions where the central Ag(II) atom is reduced to homogenously dispersed silver nanoparticles in the polymer matrix.
The following 2 [dmaphPcAg] 0 photoinitiation mechanism was proposed [23]: The photoexcited [dmaphPcAg]* is formed via irradiation in the first step Subsequently, a hydrogen-transfer reaction between p [dmaphPcAg] +• and 2 [dmaphPcAg] 0 leads to dehydrogenated aromatic-derived aminoalkyl radicals s [dmaphPcAg − H] q• and Brønsted photoacids 1 H + according to Equation ( 4) The Brønsted acids subsequently initiate ring-opening reactions in epoxides.r [dmaphPc] −• and s [dmaphPcAg − H] q• initiate the FRP of acrylates.Nevertheless, the above FRP mechanism (1)-( 4) has several limitations.Whereas 2 [dmaphPcAg] 0 and m [dmaphPcAg] 0 * have an odd number of electrons and their doublet ground spin state corresponds to natural radicals, n [dmaphPcAg] − , p [dmaphPcAg] + , and the monodehydrogenated species s [dmaphPcAg − H] 0 have an even number of electrons and thus can form biradicals.These correspond to singlet or triplet spin states, but the singlet biradicals are not detectable by EPR measurements.Consequently, quantum-chemical calculations are necessary to describe their spin densities.In [23], only quantum-chemical calculations of neutral 2 [dmaphPcAg] 0 in doublet spin state and neutral 1 [dmaphPcH 2 ] 0 in singlet spin state were performed.In our more recent (TD-)B3LYP study [24], optimal geometries, electronic structure, and electron transitions of m [dmaphPcAg] q species in vacuum with charges q = +1 to −2 in the two lowest spin states m were investigated from the point of view of the Jahn-Teller effect.However, this study was not related to spin distribution in the m [dmaphPcAg] q species.
The aim of our current study is to complete the previous studies on DFT calculations of m [dmaphPcAg] q species in CHCl 3 with various charges, q, corresponding to silver oxidation states between +III and 0 and in the two lowest spin states, m.We set to describe their electron-and spin-density distributions.To complete the picture, we also studied the dehydrogenated/deprotonated 1 [dmaphPcH 2 ] 0 species in the lowest spin state.We hope that the obtained results on electronic structure, energetics, and electron transitions will contribute to the verification of the above-mentioned reaction mechanism (1)-(3) [23].

Results
Geometry optimization of m [dmaphPcAg] q complexes in CHCl 3 in two lowest spin states without any symmetry restriction (see below) started from their optimized structures in vacuum obtained in [24].After suitable modifications, these structures were used as starting structures for analogous geometry optimizations of dehydrogenated/deprotonated species m [dmaphPcH 2 ] q in the lowest two spin states as well.Although the singlet spin states of the systems under study were treated using an unrestricted formalism (the 'broken symmetry' treatment [25]), no spin-polarized solutions were obtained, i.e., their energies are identical to the case of restricted DFT calculations.Gibbs energies and relevant geometry parameters of the stable structures are presented in Tables 1-3.

Gibbs Energies
According to the Gibbs energy data calculated at room temperature (Table 1), the energies of the m [dmaphPcAg] q complexes decrease upon reduction.However, even the structures of the m [dmaphPcAg] 2− complexes corresponding to the formal oxidation state Ag(0) seem to be stable.Except for 3 [dmaphPcAg] + , the complexes in lower spin states are more stable.It implies that the 3 [dmaphPcAg] + biradical can be present in non-vanishing concentrations in the reaction system.Consequently, reaction (2) is correct.Despite the relative concentrations of the deexcitation products of the excited m [dmaphPcAg] 0 * species not necessarily satisfy the Boltzmann distribution law, our results indicate that only 1 [dmaphPcAg] − and 3 [dmaphPcAg] − species can co-exist in comparable concentrations.In equilibria, the remaining m [dmaphPcAg] q complexes with the same charges are present only in the more stable form because of the extremely large energy difference between their spin states.Therefore, if the LED@385 nm irradiation (corresponding to 310.7 kJ/mol energy) is fully absorbed by 2 [dmaphPcAg] 0 excitation, reaction (2) is shifted to the right in agreement with [23] (the reaction Gibbs energy of −26.5 kJ/mol at 298 K).
According to the data in Table 1, deprotonated m [dmaphPcH n ] q species, n = 2 or 1, seem to be more stable than their dehydrogenated counterparts (i.e., with q preserved).However, their relative stability is also dependent on the reactions of their formation.The reaction Gibbs energy of 2 Ag 0 formation (with atomic Gibbs energy of −146.98864Hartree) according to reaction (3) is highly positive (+235.0kJ/mol for 3 [dmaphPcAg] − and +240.7 kJ/mol for 1 [dmaphPcAg] − ) and its equilibrium is shifted right due to subsequent formation and precipitation of silver nanoparticles.Due to the lack of necessary data, we deal only with the (1)-(3) reaction equilibria.

DFT-Optimized Structures
The DFT-optimized geometries of the m [dmaphPcAg] q complexes are very similar to the 2 [dmaphPcAg] 0 structure presented in Figure 1.Except for the dimethylphenyl groups, all m [dmaphPcAg] q structures are planar, only the central Ag atom might be slightly above the plane of four pyridine nitrogen atoms N py (up to 0.019 Å in 3 [dmaphPcAg] + , see Table 2).The values of the lengths of the Ag-N py bonds, as well as of the N py -Ag-N py angles indicate that the C 4 symmetry axis is preserved in all the silver complexes, except 4 [dmaphPcAg] 0 , 1 [dmaphPcAg] − , and 3 [dmaphPcAg] − .The Ag-N py bond lengths increase with complex reduction up to 1 [dmaphPcAg] − only.Therefore, the electron density transfer to Ag is not related to its out-of-plane movement.
The DFT-optimized structures of m [dmaphPcH n ] q , n = 2 → 0, are presented in Figures 2-4, S3 and S4, and in Table 3. Except for 1 [dmaphPcH] − , their phthalocyanine cores are planar.Their H-N py bond lengths increase during deprotonation/dehydrogenation of the central ring.Due to H-N py bonds, the C 4 symmetry axis can be observed only in 2 [dmaphPc] − and 1 [dmaphPc] 2− .equilibria, the remaining m [dmaphPcAg] q complexes with the same charges are present only in the more stable form because of the extremely large energy difference between their spin states.Therefore, if the LED@385 nm irradiation (corresponding to 310.7 kJ/mol energy) is fully absorbed by 2 [dmaphPcAg] 0 excitation, reaction (2) is shifted to the right in agreement with [23] (the reaction Gibbs energy of −26.5 kJ/mol at 298 K).
According to the data in Table 1, deprotonated m [dmaphPcHn] q species, n = 2 or 1, seem to be more stable than their dehydrogenated counterparts (i.e., with q preserved).However, their relative stability is also dependent on the reactions of their formation.The reaction Gibbs energy of 2 Ag 0 formation (with atomic Gibbs energy of −146.98864Hartree) according to reaction (3) is highly positive (+235.0kJ/mol for 3 [dmaphPcAg] − and +240.7 kJ/mol for 1 [dmaphPcAg] − ) and its equilibrium is shifted right due to subsequent formation and precipitation of silver nanoparticles.Due to the lack of necessary data, we deal only with the (1)-(3) reaction equilibria.

DFT-Optimized Structures
The DFT-optimized geometries of the m [dmaphPcAg] q complexes are very similar to the 2 [dmaphPcAg] 0 structure presented in Figure 1.Except for the dimethylphenyl groups, all m [dmaphPcAg] q structures are planar, only the central Ag atom might be slightly above the plane of four pyridine nitrogen atoms Npy (up to 0.019 Å in 3 [dmaphPcAg] + , see Table 2).The values of the lengths of the Ag-Npy bonds, as well as of the Npy-Ag-Npy angles indicate that the C4 symmetry axis is preserved in all the silver complexes, except 4 [dmaphPcAg] 0 , 1 [dmaphPcAg] − , and 3 [dmaphPcAg] − .The Ag-Npy bond lengths increase with complex reduction up to 1 [dmaphPcAg] − only.Therefore, the electron density transfer to Ag is not related to its out-of-plane movement.

Electronic Structure Characteristics
The main features of the m [dmaphPcAg] q complexes are presented in Figures 5-7 and S5-S7, and Table 2. Their Ag-N py bond orders and positive Ag charges decrease upon reduction up to m [dmaphPcAg] − .Except for complexes in singlet spin states, the d-electron populations of silver atoms are practically constant.The atomic charges of the pyrrole nitrogen N py are more negative than those of the bridging nitrogen N br , and the amine nitrogen N amin has even fewer negative charges.During the reduction of the complex, all N charges become even more negative.Positive charges of carbon atoms at the 4-and 7-positions of the isoindole units denoted as C α decrease with the reduction of the complex.Similarly, small negative charges of carbon atoms at isoindoles 5-and 6-positions denoted as C β increase with the reduction of the complex.Significantly more negative charges of the C met methyl carbons do not depend on the charge q and spin state m of the m [dmaphPcAg] q complexes.Only N amin and C met charges were not affected by the lower symmetry of the complexes studied.
S7, and Table 2. Their Ag-Npy bond orders and positive Ag charges decrease upon reduction up to m [dmaphPcAg] − .Except for complexes in singlet spin states, the d-electron populations of silver atoms are practically constant.The atomic charges of the pyrrole nitrogen Npy are more negative than those of the bridging nitrogen Nbr, and the amine nitrogen Namin has even fewer negative charges.During the reduction of the complex, all N charges become even more negative.Positive charges of carbon atoms at the 4-and 7-positions of the isoindole units denoted as Cα decrease with the reduction of the complex.Similarly, small negative charges of carbon atoms at isoindoles 5-and 6-positions denoted as Cβ increase with the reduction of the complex.Significantly more negative charges of the Cmet methyl carbons do not depend on the charge q and spin state m of the m [dmaphPcAg] q complexes.Only Namin and Cmet charges were not affected by the lower symmetry of the complexes studied.
The highest spin density at Ag atoms decreases only slightly with reduction.Npy atoms have ca two-three times lower spin density of the same sign, which rises with reduction.In both cases, the spin density increases with spin multiplicity.Except for 4 [dmaphP-cAg] 2− , the spin density of the opposite sign at Nbr atoms is about one order lower and of variable signs.The spin density at Cα atoms is relevant only in anionic complexes and in higher spin states.Cβ atoms have even lower spin density.The spin density at Namin and Cmet atoms is vanishing.Only the Nbr, Namin, and Cmet charges were not affected by the lower symmetry of the complexes under study.Except for 3 [dmaphPcAg] + , only vanishing spin density can be found in dimethylaminophenyl groups.The highest spin density at Ag atoms decreases only slightly with reduction.N py atoms have ca two-three times lower spin density of the same sign, which rises with reduction.In both cases, the spin density increases with spin multiplicity.Except for 4 [dmaphPcAg] 2− , the spin density of the opposite sign at N br atoms is about one order lower and of variable signs.The spin density at C α atoms is relevant only in anionic complexes and in higher spin states.C β atoms have even lower spin density.The spin density at N amin and C met atoms is vanishing.Only the N br , N amin , and C met charges were not affected by the lower symmetry of the complexes under study.Except for 3 [dmaphPcAg] + , only vanishing spin density can be found in dimethylaminophenyl groups.The main features of the m [dmaphPcH n ] q species are presented in Figures S8 and S9 and Table 3.The H-N py bond orders decrease with dehydrogenation/deprotonation.The same trend is exhibited by the most negative N py charges, whereas the N br ones exhibit the reverse trend.The even less negative N amin charges increase with the negative charge of the whole species.The positive C α charges decrease with the total charge of the species and increase with deprotonation/dehydrogenation.Only small changes in the very small C β charges can be observed.Negative C met charges are constant in all m [dmaphPcH n ] q species under study and are equal to those of m [dmaphPcAg] q .
We had only two2 [dmaphPcH n ] q species with non-zero spin.The small spin densities at the N py and N br atoms are of the same sign, unlike the higher ones at C α atoms.The vanishing spin density is at C β and N amin atoms.No spin density was observed at C met atoms.

TD-DFT Calculated Electron Transitions
In this section we will compare the TD-DFT-calculated electron transitions of m [dmaphPcAg] q complexes in CHCl 3 (Figures S10-S17, Table 4) with UV-vis spectra of 2 [dmaphPcAg] 0 in CHCl 3 before and during photolysis (Figures S1 and S2, Table 4).
Table 4. Wavelengths of the measured UV-vis peaks, λ exp (m, medium; s, strong; sh, shoulder) [23], and possible assignments of the TD-DFT-calculated wavelength of the corresponding electron transitions, λ calc (oscillator strengths in parentheses) for the compounds studied in CHCl 3 .The assignments, which are not excluded by missing electron transitions (see text), are denoted in bold.

Discussion
Two-or even three-electron reduction of the 3 [dmaphPc] + species causes only small changes in the electron and spin population at the central Ag atom, and the same holds for the Ag-N py bonds.The added electrons are prevailingly distributed over the dmaphPc 2− ligand only, which is typical for 'non-innocent' ligands.This reduction does not cause a shift of Ag from the phthalocyanine plane.However, neutral Ag nanoparticles should be formed within the endothermic reaction (3), which is simultaneously connected with ca.0.8 electron addition to Ag with its move from the ligand plane.The planarity of the phthalocyanine core of 2 [dmaphPc] − is preserved.These changes should proceed in several reaction steps, including the aggregation of the [dmaphPcAg] − species in the solution.
The results of our 'broken symmetry' DFT calculations indicate the nonexistence of singlet biradicals.According to the energy data, the 3 [dmaphPcAg] + concentration should dominate over their singlet counterparts, but the UV-vis spectra [23] do not confirm their presence in reaction systems.Based on EPR measurements, this can be explained by the very low stability of 3 [dmaphPcAg] + , which was detected using spin traps only [23].Moreover, only this species has a non-vanishing spin density at N amin atoms (see Figure 5) as proposed in [23].The calculated electron transitions of the EPR silent 1 [dmaphPcAg] + species do not agree with UV-vis spectra [23] and so it is not present in reaction solutions.
The presence of 2 [dmaphPcAg] 0 in reaction solutions is in agreement with the DFT and TD-DFT calculations as well as with the EPR and UV-vis measurements [23].Comparison of UV-vis spectra with the TD-DFT electron transition and the DFT energy data indicate the absence of 4 [dmaphPcAg] 0 in reaction solutions.
The coexistence of 1 [dmaphPcAg] − and 3 [dmaphPcAg] − in reaction solutions is allowed by their energies and by the agreement of the calculated electron transitions with UV-vis spectra [23]. 1 [dmaphPcAg] − is EPR silent.
Energy data indicate that the concentration of 2 [dmaphPcAg] 2− should dominate over that of 4 [dmaphPcAg] 2− but the calculated electron transitions of both species do not agree with UV-vis spectra [23], implying their absence in reaction solutions.
However, the calculated electron transitions cannot explain all the spectral peaks in Figure S2, such as the shoulder at 450 nm.In [23], it was ascribed to silver surface plasmon resonance of silver nanoparticles.Simple TD-DFT calculations cannot describe the corresponding electron transition and vibronic interactions must be included for this purpose.Unfortunately, we are not able to conduct such calculations for technical reasons.

Methods
The geometries of m [dmaphPcAg] q , with charges q = −2 to +1 in the two lowest spin states (defined by spin multiplicities) m, and m [dmaphPcH n ] q , n = 2 to 0, q = 0, 1, or 2, in the lowest spin states m, in CHCl 3 solutions were optimized using the standard B3LYP [26] hybrid functional with Grimme's GD3 dispersion correction [27].The cc-pVDZ-PP pseudopotential and basis set for Ag [28] and cc-pVDZ basis sets for the remaining atoms [29] were used for this purpose in terms of an unrestricted formalism within the 'broken symmetry' treatment [25].The SMD (Solvation Model based on solute electron Density) modification [30] of the integral equation formalism polarizable continuum model was used to account for solvent effects.The optimized structures were tested for the absence of imaginary vibrations using vibrational analysis.The time-dependent DFT method (TD-DFT) [31] for 90-120 states was used to evaluate the excited state energies and the intensities of the corresponding electron transitions.The electronic structure was evaluated in terms of Natural Bond Orbital (NBO) population analysis [32].The Gaussian16 [33] program package was used to perform all quantum-chemical calculations.

Conclusions
This study aimed to supplement the quantum-chemical studies related to the 2 [dmaphPcAg] 0 photoinitiator of polymerization reactions in [23].We investigated the initial steps (1)-( 3) of FRP proposed in [23] via TD-DFT interpretation of the EPR and UV-vis measurements by verifying the presence of possible reaction intermediates m [dmaphPcAg] q , q = 1 → −2, 1 [dmaphPcH 2 ] 0 and its deprotonation/dehydrogenation products in the irradiated reaction system.
Our results suggest the presence of crucial unstable 3 [dmaphPcAg] + species, which was deduced by EPR spin trap experiments [23]; however, its identification was complicated due to the presence of other similar compounds in reaction solutions.
However, the formation of silver nanoparticles by reaction (3) may be a weak point of the proposed reaction mechanism from the energetic, stereochemistry, and electronic structure points of view.Unfortunately, we do not have sufficient information to propose any alternative reaction mechanisms.Further experimental and theoretical studies are desirable in this field.
[dmaphPcH] − ,2 [dmaphPcH] 0 ,1 [dmaphPc] 2− , and2 [dmaphPc] − in CHCl 3 .Funding:This research has been supported by the Slovak Research and Development Agency (project no.APVV-19-0087), by the Slovak Scientific Grant Agency VEGA (project no.1/0175/23), and by the Ministry of Education, Science, Research and Sport of the Slovak Republic within the scheme "Excellent research teams".The author thanks the HPC center at the Slovak University of Technology in Bratislava, which is a part of the Slovak Infrastructure of High-Performance Computing (SIVVP project ITMS 26230120002, funded by European Region Development Funds) for the computational time and resources made available.Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.