We report the results of theoretical calculations on the optimized structures and relative energies between the D4d and D2 symmetry structures for double-decker type phthalocyanine compounds, Ti(Pc)2, Ti(Pc)2+, Sn(Pc)2, Sn(Pc)2+, Sc(Pc)2 and Sc(Pc)2+, using eighteen types of functionals: B3LYP, B3PW91, B3P86, PBE1PBE, BHandHLYP, BPW91, BP86, M06, M06-2x, M06-HF, M06L, LC-BPW91, LC-ωPBE, CAM-B3LYP, B97D, ωB97, ωB97X and ωB97XD. Two phthalocyanine moieties are stacked in a face-to-face configuration in the D4d structure, but they are stapled by two σ-bonds in the D2 one. We found that the molecular symmetry of M(Pc)2 and M(Pc)2+ depends on the balance between stabilization due to electron delocalization and exchange repulsion of π-electrons in the phthalocyanine moieties. We assessed the performance of the well-established functionals to select the appropriate functional for calculations on M(Pc)2 and M(Pc)2+, and several important aspects came out. Generally, the hybrid GGA and hybrid meta-GGA functionals with 20–27% of the HF exchange term would give the molecular structures consistent with the experimental expectations for the double-decker type phthalocyanine compounds. Pure GGA and pure meta-GGA functionals (BPW91, BP86, M06L and B97D) have the tendency to overestimate the stability of the D4d structure. On the other hand, functionals including HF exchange for 50% and over or including long-range corrections (BHandHLYP, M06, M06-2x, M06-HF, LC-BPW91, LC-ωPBE, CAM-B3LYP, ωB97, ωB97X and ωB97XD) tend to overestimate the stability of the D2 structure. It should be emphasized that the B3LYP functional, one of the most commonly used hybrid GGA functionals with 20% HF exchange, cannot estimate the relative stability between the two molecular structures of Ti(Pc)2 appropriately. The calculation for the systems considered in this article required well-balanced treatment of the HF exchange with the accompanied exchange–correlation functional. Thus, as has been pointed out rigorously and frequently, the selection of the functional is a crucial point for reliability of the calculations.

The molecular geometries, electronic structures, and excitation energies of tin and lead phthalocyanine compounds, SnPc, PbPc, Sn(Pc)2, and Pb(Pc)2, were investigated using the B3LYP method within a framework of density functional theory (DFT). The geometries of SnPc, PbPc, Sn(Pc)2, and Pb(Pc)2 were optimized under C4v, C4v, D4d, and D4d molecular symmetries, respectively. The excitation energies of these molecules were computed by the time-dependent DFT (TD-DFT) method. The calculated results for the excited states of three compounds other than the unknown Pb(Pc)2 corresponded well with the experimental results of electronic absorption spectroscopy. The non-planar C4v molecular structure of SnPc and PbPc influences especially on the orbital energy of the HOMO−1 through mixing of the s-type atomic orbital of the central metal atom to the π system of the Pc ring in an anti-bonding way; however, the HOMO and the LUMO have little effect of the deviation from the planar structure because they have no contribution from the atomic orbital of the central metal. This orbital mixing pushes up the orbital energy of the HOMO−1, and reduces the energy of the metal-to-ligand charge transfer band of SnPc and PbPc. The calculated results also reproduced well the excitation profile of Sn(Pc)2, which was quite different from that of SnPc. The strong interactions between the π-type orbitals of two Pc moieties altered the electronic structure resulting in the characteristic excitation profile of Sn(Pc)2. In addition, this caused a reduction of about 0.8 eV in the ionization potential as compared to usual MPcs including SnPc, which was consistent with the experimental results.

The electronic structures and absorption spectra for three different types (X, α and β) of model dimers of lithium phthalocyanine (LiPc) were investigated by the density functional theory (DFT) and compared with a LiPc monomer. We quantitatively investigated the excited states of the three LiPc dimers using time-dependent DFT calculations. The differences and similarities of the observed absorption spectra in the solution and the polymorphic solids of LiPc were clearly interpreted by the calculated excited states of the monomer and dimers. The calculated results for the dimers presumed that the X-form showed a different electronic spectral pattern from the monomer and the other two forms, whereas the α- and β-forms presented similar electronic absorption profiles to each other and to the monomer. The calculated excited states also explained the differences in absorption profiles between LiPc and typical phthalocyanine compounds. These characteristic features of LiPc would be closely related to its molecular orbitals, especially those which originated from the singly occupied molecular orbital (SOMO) of the LiPc monomer. It was shown that the next highest occupied π-type orbital to the SOMO of the monomer reduced the energy of the low-lying excited states, which corresponded to the Q- and B-bands of the dimers.Graphical abstractThe excited states were calculated using the optimized geometries of a free LiPc monomer and the three model dimers, and the obtained results will be discussed in comparison with experimental absorption spectroscopic data.Highlights► The absorption spectra for three LiPc dimers were investigated by the TD-DFT method. ► The differences and similarities in the absorption spectra between the solution and each polymorph of LiPc were clearly interpreted. ► The calculated excited states explained the differences in absorption profiles between LiPc and typical phthalocyanine compounds.

The molecular geometries, electronic structures, and excitation energies of NPh3, NPh2Me, NPhMe2, and NMe3, were investigated using DFT and post-Hartree Fock methods. When the structural stabilities of these compounds were compared to results obtained by using MP4(SDQ) method, it was confirmed that the optimized geometries by using MP2 method were sufficiently reliable. The excited states with large oscillator strengths consisted of transition components from the HOMO. It should be noted that the orbitals of the nitrogen atom mix with the π-orbital of the phenyl group in an anti-bonding way in the HOMO, and the orbital energy increases with this mixing. The unoccupied orbitals are generated from bonding and anti-bonding type interactions between the π-orbitals of the phenyl groups; therefore, the number of phenyl groups strongly affects the energy diagram of the compounds studied. The differences in the energy diagram cause a spectral change in these compounds in the ultraviolet region.Graphical abstract. The molecular geometries, stabilities, electronic structures, and excitation energies of triphenylamine and its derivatives, NPh3, NPh2Me, NPhMe2, and NMe3, were investigated using DFT and Post-Hartree Fock methods.Highlights► Physical properties of NPh3 and its derivatives have been studied. ► Excited states with large oscillator strengths consisted of transitions from HOMO. ► The number of phenyl groups strongly affects the energy diagram of the compounds. ► Differences in the energy diagram cause a spectral change in the ultraviolet region.

The effects of axial ligands on the ground-state geometries, electronic structures and the characteristic optical properties of iron phthalocyanine and its derivatives, FePc and FePcLn (L = pyridine (Py) and cyanide (CN−); n = 1, 2), were investigated using the density functional theory (DFT) method. The geometries of FePc with a triplet spin state and of FePc(Py), FePc(Py)2, FePc(CN−) and FePc(CN−)2 with singlet spin states were optimized under D4h, C2v, D2h, C4v, and D4h molecular symmetries, respectively. The highest occupied molecular orbitals (HOMOs) of FePc, FePc(Py), FePc(Py)2, and FePc(CN−) are π-type orbitals, which have no contribution from the pz atomic orbitals of all nitrogen atoms, whereas the HOMO of FePc(CN−)2 is the 7eg orbital, which has contributions from the dxz and the dyz orbitals of the Fe atom mixing with the π-orbitals of the axial CN− ligands. The time-dependent (TD) DFT method gives many optically allowed excitations for FePc, FePc(Py), FePc(Py)2, FePc(CN−), and FePc(CN−)2 in the UV-VIS region. Our calculated bands corresponded well with the experimental results. In FePc(Py)2, the metal–ligand charge transfer (MLCT) transitions from the metal d to the axial-ligand π*-type orbitals contributed to the B band region. In FePc(CN−)2, the MLCT transitions from the metal d to the Pc-ring π*-type orbitals contributed mainly to the first B band region, but those from the metal d to the axial-ligand π*-type orbitals did not appear in the energy regions of the Q and B bands. Thus, the axial ligands caused a spectral change in FePc through orbital mixing.

A recent papar by Lui et al. [Z. Liu, X. Zhang, Y. Zhang, J. Jiang, Spectrochim. Acta A 67 (2007) 1232] reported on the theoretical investigations of the fully optimized geometries and electronic structures of iron (II) phthalocyanine (FePc) with the singlet spin state carried out with the restricted density functional theory (DFT) method, where the B3LYP functional was adopted for the exchange-correlation term; however, the triplet spin state was experimentally reported, and we also obtained the triplet spin state by the unrestricted DFT calculations.

The molecular geometries, electronic structures, and excitation energies of tin and lead phthalocyanine compounds, SnPc, PbPc, Sn(Pc)2, and Pb(Pc)2, were investigated using the B3LYP method within a framework of density functional theory (DFT). The geometries of SnPc, PbPc, Sn(Pc)2, and Pb(Pc)2 were optimized under C4v, C4v, D4d, and D4d molecular symmetries, respectively. The excitation energies of these molecules were computed by the time-dependent DFT (TD-DFT) method. The calculated results for the excited states of three compounds other than the unknown Pb(Pc)2 corresponded well with the experimental results of electronic absorption spectroscopy. The non-planar C4v molecular structure of SnPc and PbPc influences especially on the orbital energy of the HOMO−1 through mixing of the s-type atomic orbital of the central metal atom to the π system of the Pc ring in an anti-bonding way; however, the HOMO and the LUMO have little effect of the deviation from the planar structure because they have no contribution from the atomic orbital of the central metal. This orbital mixing pushes up the orbital energy of the HOMO−1, and reduces the energy of the metal-to-ligand charge transfer band of SnPc and PbPc. The calculated results also reproduced well the excitation profile of Sn(Pc)2, which was quite different from that of SnPc. The strong interactions between the π-type orbitals of two Pc moieties altered the electronic structure resulting in the characteristic excitation profile of Sn(Pc)2. In addition, this caused a reduction of about 0.8 eV in the ionization potential as compared to usual MPcs including SnPc, which was consistent with the experimental results.

The effects of axial ligands on the ground-state geometries, electronic structures and the characteristic optical properties of iron phthalocyanine and its derivatives, FePc and FePcLn (L = pyridine (Py) and cyanide (CN−); n = 1, 2), were investigated using the density functional theory (DFT) method. The geometries of FePc with a triplet spin state and of FePc(Py), FePc(Py)2, FePc(CN−) and FePc(CN−)2 with singlet spin states were optimized under D4h, C2v, D2h, C4v, and D4h molecular symmetries, respectively. The highest occupied molecular orbitals (HOMOs) of FePc, FePc(Py), FePc(Py)2, and FePc(CN−) are π-type orbitals, which have no contribution from the pz atomic orbitals of all nitrogen atoms, whereas the HOMO of FePc(CN−)2 is the 7eg orbital, which has contributions from the dxz and the dyz orbitals of the Fe atom mixing with the π-orbitals of the axial CN− ligands. The time-dependent (TD) DFT method gives many optically allowed excitations for FePc, FePc(Py), FePc(Py)2, FePc(CN−), and FePc(CN−)2 in the UV-VIS region. Our calculated bands corresponded well with the experimental results. In FePc(Py)2, the metal–ligand charge transfer (MLCT) transitions from the metal d to the axial-ligand π*-type orbitals contributed to the B band region. In FePc(CN−)2, the MLCT transitions from the metal d to the Pc-ring π*-type orbitals contributed mainly to the first B band region, but those from the metal d to the axial-ligand π*-type orbitals did not appear in the energy regions of the Q and B bands. Thus, the axial ligands caused a spectral change in FePc through orbital mixing.

We report the results of theoretical calculations on the optimized structures and relative energies between the D4d and D2 symmetry structures for double-decker type phthalocyanine compounds, Ti(Pc)2, Ti(Pc)2+, Sn(Pc)2, Sn(Pc)2+, Sc(Pc)2 and Sc(Pc)2+, using eighteen types of functionals: B3LYP, B3PW91, B3P86, PBE1PBE, BHandHLYP, BPW91, BP86, M06, M06-2x, M06-HF, M06L, LC-BPW91, LC-ωPBE, CAM-B3LYP, B97D, ωB97, ωB97X and ωB97XD. Two phthalocyanine moieties are stacked in a face-to-face configuration in the D4d structure, but they are stapled by two σ-bonds in the D2 one. We found that the molecular symmetry of M(Pc)2 and M(Pc)2+ depends on the balance between stabilization due to electron delocalization and exchange repulsion of π-electrons in the phthalocyanine moieties. We assessed the performance of the well-established functionals to select the appropriate functional for calculations on M(Pc)2 and M(Pc)2+, and several important aspects came out. Generally, the hybrid GGA and hybrid meta-GGA functionals with 20–27% of the HF exchange term would give the molecular structures consistent with the experimental expectations for the double-decker type phthalocyanine compounds. Pure GGA and pure meta-GGA functionals (BPW91, BP86, M06L and B97D) have the tendency to overestimate the stability of the D4d structure. On the other hand, functionals including HF exchange for 50% and over or including long-range corrections (BHandHLYP, M06, M06-2x, M06-HF, LC-BPW91, LC-ωPBE, CAM-B3LYP, ωB97, ωB97X and ωB97XD) tend to overestimate the stability of the D2 structure. It should be emphasized that the B3LYP functional, one of the most commonly used hybrid GGA functionals with 20% HF exchange, cannot estimate the relative stability between the two molecular structures of Ti(Pc)2 appropriately. The calculation for the systems considered in this article required well-balanced treatment of the HF exchange with the accompanied exchange–correlation functional. Thus, as has been pointed out rigorously and frequently, the selection of the functional is a crucial point for reliability of the calculations.