Profiling energetics and spectroscopic signatures in prototropic tautomers of asymmetric phthalocyanine analogues

Density functional theory (DFT) and time-dependent density functional theory (TDDFT) were used to explain discrepancies in UV-vis and MCD spectra of the metal-free tribenzo[b,g,l]thiopheno[3,4-q]porphyrazine (1), substituted tribenzo[b,g,l]porphyrazine (2), and 2,3-bis(methylcarboxyl)phthalocyanine (3). On the basis of gas-phase and polarized continuum solvation model (PCM) DFT and TDDFT calculations, it was suggested that both NH tautomers contribute to the spectroscopic signature of 1, whereas the Q-band region of 2 and 3 is dominated by a single NH tautomer. For all tested compounds, it was found that the combination of the BP86 exchange-correlation functional, 6-31G(d) basis set, and TDDFT-PCM approach provides the best accuracy in energies of the Q(x)- and Q(y)-bands of the individual NH tautomers as well as correctly describes their relative energy differences, which are important in understanding of experimental spectroscopy of the target systems.     

Time-dependent DFT studies of metal core-electron excitations in Mn complexes

Time-dependent density functional theory (TDDFT) has been applied to study core excitations from 1s and 2p Mn orbitals in a series of manganese complexes with oxygen and nitrogen donor ligands. The effect of basis set and functional on the excitation energy was evaluated in detail for one complex, Mn(acac)2 x (H2O)2. The results obtained for a range of compounds, namely, [Mn(Im)6]Cl2, Mn(CH3COO)2 x 4 H2O, Mn(acac)3, Mn(SALADHP)2 and [Mn(SALPN)O]2, show good consistency with the data from X-ray absorption spectroscopy (XAS), confirming the relation between the Mn K-edge energy and the oxidation state of the Mn atom. The energies predicted for 2p core excitations show a dependence on the metal oxidation state very similar to that determined experimentally by 1s2p resonant inelastic X-ray scattering (RIXS) studies for Mn(acac)2 x (H2O)2, Mn(acac)3, and Mn(sal)2(bipy). The reliability of the K-edge energies obtained in the present study indicates that TDDFT can be used in determining the oxidation states of Mn atoms in different computational models of the manganese cluster of photosystem II (PSII).     

Role of polyols (erythritol, xylitol and sorbitol) on the structural stabilization of collagen

A state-specific scheme for time-dependent density functional theory (SS-TDDFT) based on the Davidson algorithm is presented. SS-TDDFT is a method devised for speeding up TDDFT calculations by screening transitions that contribute to a specific excitation. By applying this method to calculations of the low-lying excitation energies of test molecules (N₂, CO, H₂CO, C₂H₄ and C₆H₆), water clusters and polyenes, we found that SS-TDDFT accurately reproduced the excitation energies of standard TDDFT while drastically reducing the rank of the TDDFT response matrix without loss of accuracy. We have thus formulated TDDFT that works more efficiently and economically for memory storage.     

Electronic transitions in [Re6S8X6](4-) (X = Cl, Br, I): results from time-dependent density functional theory and solid-state calculations

Relativistic time-dependent density functional theory (TDDFT) calculations were performed on the excited states of the [Re6S8X6](4-) (X = Cl, Br, I) series. For all members of the series, the lowest excited states in the spectra do not correspond to a ligand-to-metal (or ligand-to-cluster) excitation but rather a cluster-cluster transition from the HOMO e(g) to antibonding t(1u) orbitals with only a modest admixture of Re-X sigma* character. These results lead to a re-evaluation of the role of the axial ligand in these compounds. The calculated excitation energies reproduce the experimental absorption and emission spectra. This work also confirms previous TDDFT calculations on the emission energies. Results for discrete cluster ions are compared with those obtained from calculations in the solid state in Cs4[Re6S8X6].CsX (X = Cl, Br) and Cs4[Re6S8I6].2CsI. Significant differences are seen in the relatively higher energies of the antibonding t(1u) orbital in the solid-state case, and an inversion in the orbital character of the two allowed absorptions is calculated. The e(g) (HOMO)-to-a(2g) (LUMO) orbital energy differences corresponding to the emission transition are quite comparable for the solid state and discrete cluster calculations, and both overestimate the observed emission energy by the same margin.     

Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential

In this study we have introduced a formulation of time-dependent density functional theory (TDDFT) based on a noncollinear exchange-correlation potential. This formulation is a generalization of conventional TDDFT. The form of this formulation is exactly the same as that of the conventional TDDFT for the excitation energies of transitions that do not involve spin flips. In addition, this noncollinear TDDFT formulation allows for spin-flip transitions. This feature makes it possible to resolve more fully excited state spin multiplets, while for closed-shell systems, the spin-flip transitions will result in singlet-triplet excitations and this excitation energy calculated from this formulation of TDDFT is exactly the same as that from ordinary TDDFT. This formulation is applied to the dissociation of H(2) in its (1)Sigma(g) (+) ground state and (1)Sigma(u) (+) and (3)Sigma(u) (-) excited states with (3)Sigma(u) (-) (M(s)=+1) as the reference state and the multiplets splitting of some atoms.     

Spin-orbit relativistic long-range corrected time-dependent density functional theory for investigating spin-forbidden transitions in photochemical reactions

A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.     

A simplified relativistic time-dependent density-functional theory formalism for the calculations of excitation energies including spin-orbit coupling effect

In the present work we have proposed an approximate time-dependent density-functional theory (TDDFT) formalism to deal with the influence of spin-orbit coupling effect on the excitation energies for closed-shell systems. In this formalism scalar relativistic TDDFT calculations are first performed to determine the lowest single-group excited states and the spin-orbit coupling operator is applied to these single-group excited states to obtain the excitation energies with spin-orbit coupling effects included. The computational effort of the present method is much smaller than that of the two-component TDDFT formalism and this method can be applied to medium-size systems containing heavy elements. The compositions of the double-group excited states in terms of single-group singlet and triplet excited states are obtained automatically from the calculations. The calculated excitation energies based on the present formalism show that this formalism affords reasonable excitation energies for transitions not involving 5p and 6p orbitals. For transitions involving 5p orbitals, one can still obtain acceptable results for excitations with a small truncation error, while the formalism will fail for transitions involving 6p orbitals, especially 6p1/2 spinors.     

Investigation of the electronic spectra and excited-state geometries of poly(para-phenylene vinylene) (PPV) and poly(para-phenylene) (PP) by the symmetry-adapted cluster configuration interaction (SAC-CI) method

The symmetry-adapted cluster-configuration interaction (SAC-CI) method has been used to investigate the optical and geometric properties of the oligomers of poly(para-phenylene vinylene) (PPV) and poly(para-phenylene) (PP). Vertical singlet and triplet absorption spectra and emission spectra have been calculated accurately; the mean average deviation from available experimental results lies within 0.2 eV. The chain length dependence of the transition energies has been improved in comparison to earlier TDDFT and MRSDCI calculations. The present analysis suggests that conventional TDDFT with the B3LYP functional should be used carefully, as it can provide inaccurate estimates of the chain length dependence of the excitation energies of these molecules with long pi conjugation. The T1 state was predicted to be at a lower energy, by 1.0-1.5 eV for PPV and by 0.9-1.7 eV for PP, than the S1 state, which indicates a localized T1 state with large exchange energy. By calculating the SAC-CI electron density difference between the ground and excited states, the geometry relaxations due to excitations can be analyzed in detail using electrostatic force theory. For trans-stilbene, the doubly excited 21Ag state was studied, and the calculated transition energy of 4.99 eV agrees very well with the experimental value of 4.84 eV. In contrast to previous ab initio calculations, we predict this doubly excited 21Ag state to lie above the 11Bu state.     

Determination of absolute configuration using concerted ab Initio DFT calculations of electronic circular dichroism and optical rotation: bicyclo[3.3.1]nonane diones

The concerted use of ab initio time-dependent density functional theory (TDDFT) calculations of transparent spectral region optical rotation and of circular dichroism has recently become practicable, permitting the concerted use of transparent spectral region optical rotation and circular dichroism in determining the absolute configurations of chiral molecules. Here, we report concerted TDDFT calculations of the transparent spectral region specific rotations and of the circular dichroism spectra originating in n --> pi C=O group excitations of four bicyclo[3.3.1]nonane diones, 1-4. Comparison to experiment yields absolute configurations for 1-4. For each dione, specific rotations and circular dichroism spectra give identical absolute configurations. Our results are consistent with previous work, with the exception of the Octant Rule-derived absolute configuration of the 2,9-dione.     

Performance of the M11 and M11-L density functionals for calculations of electronic excitation energies by adiabatic time-dependent density functional theory

Adiabatic time-dependent density functional theory is a powerful method for calculating electronic excitation energies of complex systems, but the quality of the results depends on the choice of approximate density functional. In this article we test two promising new density functionals, M11 and M11-L, against databases of 214 diverse electronic excitation energies, and we compare the results to those for 16 other density functionals of various kinds and to time-dependent Hartree-Fock. Charge transfer excitations are well known to be the hardest challenge for TDDFT. M11 is a long-range-corrected hybrid meta-GGA, and it shows better performance for charge transfer excitations than any of the other functionals except M06-HF, which is a specialized functional that does not do well for valence excitations. Several other long-range-corrected hybrid functionals also do well, and we especially recommend M11, ωB97X, and M06-2X for general spectroscopic applications because they do exceptionally well on ground-state properties as well as excitation energies. Local functionals are preferred for many applications to extended systems because of their significant cost advantage for large systems. M11-L is a dual-range local functional and-unlike all previous local functionals-it has good performance for Rydberg states as well as for valence states. Thus it is highly recommended for excitation energy calculations on extended systems.     

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.     

Optical and photophysical properties of indolocarbazole derivatives

We present a study of the optical and photophysical properties of five ladder indolo[3,2-b]carbazoles, namely, M1, M2, M3, M4, and M5. The ground-state optimized structures were obtained by B3LYP/6-31G* density functional theory (DFT) calculations, whereas the optimization (relaxation) of the first singlet excited electronic state (S1) was performed using the restricted configuration interaction (singles) (RCIS/6-31G*) approach. The excitation to the S1 state does not cause important changes in the geometrical parameters of the compounds, as corroborated by the small Stokes shifts. The excitation and emission energies have been obtained by employing the time-dependent density functional theory (TDDFT). For all the compounds, excitation to the S1 state is weakly allowed, whereas the S2 <-- S0 electronic transition of each oligomer possesses a much larger oscillator strength. The absorption and fluorescence spectra of the compounds have been recorded in chloroform. A reasonable agreement is obtained between TDDFT vertical transition energies and the (0,0) absorption and fluorescence bands. On one hand, the pattern of the aliphatic side chains does not affect the absorption and fluorescence maxima of the compounds. On the other hand, the replacement of aliphatic chains by phenyl or thiophene rings induces hypsochromic shifts in the absorption and fluorescence spectra. Finally, the fluorescence quantum yield and lifetime of the compounds in chloroform have been obtained. From these data, the radiative and nonradiative rate constants of the deactivation of the S1 state have been determined.     

DFT-based studies on the Jahn-Teller effect in 3d hexacyanometalates with orbitally degenerate ground states

The topology of the ground-state potential energy surface of M(CN)(6) with orbitally degenerate (2)T(2g) (M = Ti(III) (t(2g)(1)), Fe(III) and Mn(II) (both low-spin t(2g)(5))) and (3)T(1g) ground states (M = V(III) (t(2g)(2)), Mn(III) and Cr(II) (both low-spin t(2g)(4))) has been studied with linear and quadratic Jahn-Teller coupling models in the five-dimensional space of the epsilon(g) and tau(2g) octahedral vibrations (Tg[symbol: see text](epsilon(g)+tau(2g)) Jahn-Teller coupling problem (T(g) = (2)T(2g), (3)T(1g))). A procedure is proposed to give access to all vibronic coupling parameters from geometry optimization with density functional theory (DFT) and the energies of a restricted number of Slater determinants, derived from electron replacements within the t(2g)(1,5) or t(2g)(2,4) ground-state electronic configurations. The results show that coupling to the tau(2g) bending mode is dominant and leads to a stabilization of D(3d) structures (absolute minima on the ground-state potential energy surface) for all complexes considered, except for [Ti(CN)(6)](3-), where the minimum is of D(4h) symmetry. The Jahn-Teller stabilization energies for the D3d minima are found to increase in the order of increasing CN-M pi back-donation (Ti(III) < V(III) < Mn(III) < Fe(III) < Mn(II) < Cr(II)). With the angular overlap model and bonding parameters derived from angular distortions, which correspond to the stable D(3d) minima, the effect of configuration interaction and spin-orbit coupling on the ground-state potential energy surface is explored. This approach is used to correlate Jahn-Teller distortion parameters with structures from X-ray diffraction data. Jahn-Teller coupling to trigonal modes is also used to reinterpret the anisotropy of magnetic susceptibilities and g tensors of [Fe(CN)(6)](3-), and the (3)T(1g) ground-state splitting of [Mn(CN)(6)](3-), deduced from near-IR spectra. The implications of the pseudo Jahn-Teller coupling due to t(2g)-e(g) orbital mixing via the trigonal modes (tau(2g)) and the effect of the dynamic Jahn-Teller coupling on the magnetic susceptibilities and g tensors of [Fe(CN)(6)](3-) are also addressed.     

Cr(CO)6 photochemistry: semi-classical study of UV absorption spectral intensities and dynamics of photodissociation

The UV absorption spectrum of Cr(CO)(6) (chromium hexacarbonyl) in gas phase is investigated by theoretical methods with focus on the absorption intensities. It is shown that in spite of good predictions for the excitation energies, the most frequently employed methods for excited-state calculations produce poor predictions for oscillator strengths and absorption cross sections. In particular, time-dependent DFT predicts relative intensities for the two main spectral bands to be up to five times larger than the experimental results depending on the functional. The best results are obtained by a multireference configuration interaction method based on DFT (DFT/MRCI). Spectral shoulders caused by vibronic-coupling absorption are assigned based on symmetry-restricted spectrum simulations. The dynamics of Cr(CO)(6) photodissociation was also considered at TDDFT/B3LYP level. The estimated time constants for the Cr(CO)(6) relaxation and dissociation are in excellent agreement with experimental values. The time constant for internal conversion, however, is longer than the experimentally observed by factor 2, presumably due to an underestimation of the experimental analysis.     

Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores

Almost all time-dependent density-functional theory (TDDFT) calculations of excited states make use of the adiabatic approximation, which implies a frequency-independent exchange-correlation kernel that limits applications to one-hole/one-particle states. To remedy this problem, Maitra et al. [N.T. Maitra, F. Zhang, R.J. Cave, K. Burke, Double excitations within time-dependent density functional theory linear response theory, J. Chem. Phys. 120 (2004) 5932 ] proposed dressed TDDFT (D-TDDFT), which includes explicit two-hole/two-particle states by adding a frequency-dependent term to adiabatic TDDFT. This paper offers the first extensive test of D-TDDFT, and its ability to represent excitation energies in a general fashion. We present D-TDDFT excited states for 28 chromophores and compare them with the benchmark results of Schreiber et al. [M. Schreiber, M.R. Silva-Junior, S.P.A. Sauer, W. Thiel, Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3, J. Chem. Phys. 128 (2008) 134110]. We find the choice of functional used for the A-TDDFT step to be critical for positioning the 1h1p states with respect to the 2h2p states. We observe that D-TDDFT without HF exchange increases the error in excitations already underestimated by A-TDDFT. This problem is largely remedied by implementation of D-TDDFT including Hartree-Fock exchange.     

Stepwise construction of manganese-chromium carbonyl chalcogenide complexes: synthesis, electrochemical properties, and computational studies

When trigonal-bipyramidal clusters, [PPN][E(2)Mn(3)(CO)(9)] (E = S, Se), were treated with Cr(CO)(6) and PPNCl in a molar ratio of 1:1:2 or 1:2:2 in 4 M KOH/MeCN/MeOH solutions, mono-Cr(CO)(5)-incorporated HE(2)Mn(3)-complexes [PPN](2)[HE(2)Mn(3)Cr(CO)(14)] (E = S, [PPN](2)[1a]; Se, [PPN](2)[1b]), respectively, were formed. X-ray crystallographic analysis showed that 1a and 1b were isostructural and each displayed an E(2)Mn(3) square-pyramidal core with one of the two basal E atoms externally coordinated with one Cr(CO)(5) group and one Mn-Mn bond bridged by one hydrogen atom. However, when the TMBA(+) salts for [E(2)Mn(3)(CO)(9)](-) were mixed with Cr(CO)(6) in a molar ratio of 1:1 in 4 M KOH/MeOH solutions and refluxed at 60 °C, mono-Cr(CO)(3)-incorporated E(2)Mn(3)Cr octahedral clusters [TMBA](3)[E(2)Mn(3)Cr(CO)(12)] (E = S, [TMBA](3)[2a]; Se, [TMBA](3)[2b]), respectively, were obtained. Clusters 2a and 2b were isostructural, and each consisted of an octahedral E(2)Mn(3)Cr core, in which each Mn-Mn or Mn-Cr bond of the Mn(3)Cr plane was semibridged by one carbonyl ligand. Clusters 1a and 1b (with [TMBA] salts) underwent metal core closure to form octahedral clusters 2a and 2b upon treatment with KOH/MeOH at 60 °C. In addition, 1a and 1b were found to undergo cluster expansion to form di-Cr(CO)(5)-incorporated HE(2)Mn(3)-clusters [HE(2)Mn(3)Cr(2)(CO)(19)](2-) (E = S, 3a; Se, 3b), respectively, upon the addition of 1 or 2 equiv of Cr(CO)(6) heated in refluxing CH(2)Cl(2). Clusters 3a and 3b were structurally related to clusters 1a and 1b, but with the other bare E atom (E = S, 3a; Se, 3b) further externally coordinated with one Cr(CO)(5) group. The nature, cluster transformation, and electrochemical properties of the mixed manganese-chromium carbonyl sulfides and selenides were systematically discussed in terms of the chalcogen elements, the introduced chromium carbonyl group, and the metal skeleton with the aid of molecular calculations at the BP86 level of the density functional theory.     

Relationship between orbital energy gaps and excitation energies for long‐chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.