Theoretical investigation of the molecular, electronic structures and vibrational spectra of a series of first transition metal phthalocyanines by Z. Liu et al

A recent paper 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.     

Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

A combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a self-consistent scheme linear in the solvent polarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the density-functional theory (DFT) and the Hartree-Fock (HF) theory. Sample calculations presented for ground-state energies, first-order ground-state properties, excitation energies, first-order excited state properties, polarizabilities, first-hyperpolarizabilities, and two-photon absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to high-level theory, such as coupled-cluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for ground-state and first-order properties. However, to obtain such accuracy an exchange-correlation functional capable of describing the diffuse Rydberg states must be chosen.     

Calculation of nonadiabatic couplings with restricted open-shell Kohn-Sham density-functional theory

This paper generalizes the recently proposed approaches for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) based on a Slater transition-state density to transitions such as singlet-singlet excitations, where a single-determinant ansatz is insufficient. The proposed approach is based on restricted open-shell Frank et al. [J. Chem. Phys. 108, 4060 (1998)] theory used to describe a spin-adapted Slater transition state. To treat the dependence of electron-electron interactions on the nuclear positions, variational linear-response density-functional perturbation theory is generalized to reference states with an orbital-dependent Kohn-Sham Hamiltonian and nontrivial occupation patterns. The methods proposed in this paper are not limited to the calculation of derivative coupling vectors, but can also be used for the calculation of other transition matrix elements. Moreover, they can be used to calculate the linear response of open-shell systems to arbitrary external perturbations in DFT.     

Hole localization in [AlO4]0 defects in silica materials

First-principles calculations based on cluster models have been performed to investigate the ground state and the optically excited states of the [AlO(4)](0) hole in alpha-quartz and in the siliceous zeolite ZSM-5. The structure and spectroscopic properties of this defect have been studied using the recently developed Becke88-Becke95 one-parameter model for kinetics (BB1K) functional of Zhao et al., [J. Phys. Chem. A 108, 2715 (2004)]. Our results show that the BB1K method is significantly more reliable and more accurate than the standard density-functional theory (DFT) functionals at reproducing the localized spin density on one oxygen atom and the hyperfine coupling constants associated with the hole. Furthermore, we find that the BB1K results are in close agreement with experiments, and with the self-interaction-free unrestricted Hartree-Fock (UHF) and unrestricted second-order M?ller-Plesset perturbation theory (UMP2) calculations. For the first time, we present results of the ground-state paramagnetic properties of the Al defect in ZSM-5. Similar to the theoretical work for defective alpha-quartz, we find that the BB1K, UHF, UHFLee-Yang-Parr, and UMP2 calculations show a localized hole on one oxygen neighboring the Al, while even the best to date thermochemically derived hybrid generalized gradient approximation density-functional, B97-2, predicts a different model where the hole is distributed over two oxygen. We have further considered the optical transitions of the [AlO(4)](0) center in alpha-quartz and ZSM-5. In both systems, our BB1K time-dependent density-functional theory (TDDFT) and configuration interaction singles (CIS) calculations predict that the most likely transition involves electron transfer from the hole-bearing oxygen to other neighboring oxygen ions. This reinforces the experimental conclusions obtained for defective alpha-quartz. Notably, the two lowest, most dominant excitation energies calculated by BB1K-TDDFT (1.99 and 3.03 eV) show excellent agreement with experiment (1.96 and 2.85 eV [B. K. Meyer, J.M. Spaeth, and J.A. Weil, J. Phys. C: Solid State Phys. 17, L31 (1987)]) clearly outperforming the CIS method and other DFT calculations available in the literature.     

High-resolution electronic spectra of ethylenedioxythiophene oligomers

The photophysical properties of a series of 3,4-ethylenedioxythiophene oligomers (OEDOT) with up to five repeat units are studied as function of conjugation length using absorption, fluorescence, phosphorescence, and triplet-triplet absorption spectroscopy at low temperature in a rigid matrix. At 80 K, a remarkably highly resolved vibrational fine structure can be observed in the all electronic spectra which reveals that the electronic structure of the oligomers strongly couples to two different vibrational modes (approximately 180 and approximately 50 meV). The energies of the 0-0 transitions in absorption, and fluorescence, phosphorescence, and triplet-triplet absorption all show a reciprocal dependence on the inverse number of repeat units. The triplet energies inferred from the phosphorescence spectra are accurately reproduced by quantum chemical DFT calculations using optimized geometries for the singlet ground state (S0) and first excited triplet state (T1). Using vibrational IR and Raman spectroscopy and quantum chemical DFT calculations for the normal modes in the ground state, we have been able to assign the vibrations that couple to the electronic structure to fully symmetric normal modes. The high-energy mode is associated with the well-known carbon-carbon bond stretch vibration, and the low-energy mode involves a deformation of the bond angles within the thiophene rings and a change of C-S bond lengths. Experimentally obtained Huang-Rhys parameters and theoretical normal mode deformations are used to analyze the geometry changes between T1 and S0 and to semiexperimentally predict the geometry in the S1 state for 2EDOT.     

Spin-spin contributions to the zero-field splitting tensor in organic triplets, carbenes and biradicals-a density functional and ab initio study

An evaluation study for the direct dipolar electron spin-spin (SS) contribution to the zero-field splitting (ZFS) tensor in electron paramagnetic resonance (EPR) spectroscopy is presented. Calculations were performed on a wide variety of organic systems where the SS contribution to the ZFS dominates over the second-order spin-orbit coupling (SOC) contribution. Calculations were performed using (hybrid) density functional theory (DFT), as well as complete active space self-consistent field (CASSCF) wave functions. In the former case, our implementation is an approximation, because we use the two-particle reduced spin-density matrix of the noninteracting reference system. In the latter case, the SS contribution is approximated by a mean-field method which, nevertheless, gives accurate results, compared to the approximation free computation of the SS part in a CASSCF framework. For the case of the triplet dioxygen molecule, it was shown that restricted open-shell density functional theory (RODFT), as well as CASSCF, can provide accurate spin-spin couplings while spin-unrestricted DFT leads to much larger errors. Furthermore, 15 organic radicals, including several 1,3 and 1,5 diradicals, dinitroxide biradicals, and even a chlorophyll a model system, were examined as test cases to demonstrate the accuracy and efficiency of our approach within a DFT framework. Accurate D values with root-mean-square deviations of 0.0035 cm(-1) were obtained. Furthermore, all trends, including those due to substituent effects, were correctly reproduced. In a different set of calculations, the polyacenes benzene, naphthalene, anthracene, and tetracene were studied. Applying DFT, the absolute D values were noticeably underestimated, but it was possible to correctly reproduce the trend to smaller D values with larger size of the systems. Finally, it was demonstrated that our approach is also well-suited for the study of carbenes. The smaller organic radicals of this work were also studied, through the use of CASSCF wave functions. This was a special advantage in the case of the triplet polyacenes, where the CASSCF approach gave better results than the DFT method. In comparing spin-restricted and spin-unrestricted results, it was shown through a natural orbital analysis and comparison to high-level ab initio calculations that even small amounts of spin polarization introduced by the unrestricted calculations lead to large deviations between the unrestricted Kohn-Sham (UKS) and restricted open-shell Kohn-Sham (ROKS) approaches. It is challenging to understand why the ROKS results show much better correlation with the experimental data.     

Density-functional and electron correlated study of five linear birefringences--Kerr, Cotton-Mouton, Buckingham, Jones, and magnetoelectric--in gaseous benzene

We present the results of an extended study of five birefringences--Kerr, Cotton-Mouton, Buckingham, Jones, and Magnetoelectric--on benzene in the gas phase. The relevant molecular quantities--first-order properties, linear, quadratic, and cubic response functions--are computed employing the density-functional theory (DFT) response theory, with a choice of functionals. In some cases, different functionals are employed for the wave-function computational step and for the subsequent analytical response calculation to determine the combination yielding at the same time the optimal energy and energy derivative results. Augmented correlation consistent basis sets of double and triple zeta quality are used. The DFT results are compared to those obtained at the Hartree-Fock level and in some cases within a coupled cluster singles and doubles electronic structure model. The study tries to assess the ability of the DFT response theory to describe a wide range of properties in a system of rather large size and high complexity. The relative strength of the five birefringences for plausible experimental conditions is determined and, when possible, comparison is made with the results of the measurements.     

Mechanism of ligand photodissociation in photoactivable [Ru(bpy)2L2]2+ complexes: a density functional theory study

A series of four photodissociable Ru polypyridyl complexes of general formula [Ru(bpy)2L2](2+), where bpy = 2,2'-bipyridine and L = 4-aminopyridine (1), pyridine (2), butylamine (3), and gamma-aminobutyric acid (4), was studied by density functional theory (DFT) and time-dependent density functional theory (TDDFT). DFT calculations (B3LYP/LanL2DZ) were able to predict and elucidate singlet and triplet excited-state properties of 1-4 and describe the photodissociation mechanism of one monodentate ligand. All derivatives display a Ru --> bpy metal-to-ligand charge transfer (MLCT) absorption band in the visible spectrum and a corresponding emitting triplet (3)MLCT state (Ru --> bpy). 1-4 have three singlet metal-centered (MC) states 0.4 eV above the major (1)MLCT states. The energy gap between the MC states and lower-energy MLCT states is significantly diminished by intersystem crossing and consequent triplet formation. Relaxed potential energy surface scans along the Ru-L stretching coordinate were performed on singlet and triplet excited states for all derivatives employing DFT and TDDFT. Excited-state evolution along the reaction coordinate allowed identification and characterization of the triplet state responsible for the photodissociation process in 1-4; moreover, calculation showed that no singlet state is able to cause dissociation of monodentate ligands. Two antibonding MC orbitals contribute to the (3)MC state responsible for the release of one of the two monodentate ligands in each complex. Comparison of theoretical triplet excited-state energy diagrams from TDDFT and unrestricted Kohn-Sham data reveals the experimental photodissociation yields as well as other structural and spectroscopic features.     

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.     

Addressing an instability in unrestricted density functional theory direct dynamics simulations

In Density Functional Theory (DFT) direct dynamics simulations with Unrestricted Hartree Fock (UHF) theory, triplet instability often emerges when numerically integrating a classical trajectory. A broken symmetry initial guess for the wave function is often used to obtain the unrestricted DFT potential energy surface (PES), but this is found to be often insufficient for direct dynamics simulations. An algorithm is described for obtaining smooth transitions between the open-shell and the closed-shell regions of the unrestricted PES, and thus stable trajectories, for direct dynamics simulations of dioxetane and its •O CH₂-CH₂ O• singlet diradical. © 2018 Wiley Periodicals, Inc.     

Excited-state properties and emission spectra of nonplanar heterocyclic helicenes

We discuss the electron-vibration coupling in mono-aza-[5]helicenes on the basis of a Franck-Condon analysis and density functional theory (DFT) calculations of the fluorescence and phosphorescence spectra measured in ethanol. The geometries of the initial states were obtained from time-dependent DFT (S(1)) and unrestricted DFT (T(1)) excited-state optimizations. In general, the position of the nitrogen atom has only a minor impact on the vibronic fine-structure in both absorption and emission. The shapes of the emission spectra from the lowest singlet and triplet states are found to be determined by contributions from multiple normal modes. The results of the calculations demonstrate how the interplay among these normal modes results in qualitatively and quantitatively different spectra for fluorescence and phosphorescence.     

Theoretical predictions of nuclear magnetic resonance parameters in a novel organo-xenon species: chemical shifts and nuclear quadrupole couplings in HXeCCH

We calibrate the methodology for the calculation of nuclear magnetic resonance (NMR) properties in novel organo-xenon compounds. The available state-of-the-art quantum-chemical approaches are combined and applied to the HXeCCH molecule as the model system. The studied properties are (129)Xe, (1)H, and (13)C chemical shifts and shielding anisotropies, as well as (131)Xe and (2)H nuclear quadrupole coupling constants. The aim is to obtain, as accurately as currently possible, converged results with respect to the basis set, electron correlation, and relativistic effects, including the coupling of relativity and correlation. This is done, on one hand, by nonrelativistic correlated ab initio calculations up to the CCSD(T) level and, on the other hand, for chemical shifts and shielding anisotropies by the leading-order relativistic Breit-Pauli perturbation theory (BPPT) with correlated ab initio and density-functional theory (DFT) reference states. BPPT at the uncorrelated Hartree-Fock level as well as the corresponding fully relativistic Dirac-Hartree-Fock method are found to be inapplicable due to a dramatic overestimation of relativistic effects, implying the influence of triplet instability in this multiply bonded system. In contrast, the fully relativistic second-order Moller-Plesset perturbation theory method can be applied for the quadrupole coupling, which is a ground-state electric property. The performance of DFT with various exchange-correlation functionals is found to be inadequate for the nonrelativistic shifts and shielding anisotropies as compared to the CCSD(T) results. The relativistic BPPT corrections to these quantities can, however, be reasonably predicted by DFT, due to the improved triplet excitation spectrum as compared to the Hartree-Fock method, as well as error cancellation within the five main BPPT contributions. We establish three computationally feasible models with characteristic error margins for future calculations of larger organo-xenon compounds to guide forthcoming experimental NMR efforts. The predicted (129)Xe chemical shift in HXeCCH is in a novel range for this nucleus, between weakly bonded or solvated atomic xenon and xenon in the hitherto characterized molecules.     

Linear-scaling formation of Kohn-Sham Hamiltonian: application to the calculation of excitation energies and polarizabilities of large molecular systems

We present calculations of excitation energies and polarizabilities in large molecular systems at the local-density and generalized-gradient approximation levels of density-functional theory (DFT). Our results are obtained using a linear-scaling DFT implementation in the program system DALTON for the formation of the Kohn-Sham Hamiltonian. For the Coulomb contribution, we introduce a modification of the fast multipole method to calculations over Gaussian charge distributions. It affords a simpler implementation than the original continuous fast multipole method by partitioning the electrostatic Coulomb interactions into "classical" and "nonclassical" terms which are explicitly evaluated by linear-scaling multipole techniques and a modified two-electron integral code, respectively. As an illustration of the code, we have studied the singlet and triplet excitation energies as well as the static and dynamic polarizabilities of polyethylenes, polyenes, polyynes, and graphite sheets with an emphasis on the trends observed with system size.     

Modeling carbon nanostructures with the self-consistent charge density-functional tight-binding method: vibrational spectra and electronic structure of C(28), C(60), and C(70)

The self-consistent charge density-functional tight-binding (SCC-DFTB) method is employed for studying various molecular properties of small fullerenes: C(28), C(60), and C(70). The computed bond distances, vibrational infrared and Raman spectra, vibrational densities of states, and electronic densities of states are compared with experiment (where available) and density-functional theory (DFT) calculations using various basis sets. The presented DFT benchmark calculations using the correlation-consistent polarized valence triple zeta basis set are at present the most extensive calculations on harmonic frequencies of these species. Possible limitations of the SCC-DFTB method for the prediction of molecular vibrational and optical properties are discussed. The presented results suggest that SCC-DFTB is a computationally feasible and reliable method for predicting vibrational and electronic properties of such carbon nanostructures comparable in accuracy with small to medium size basis set DFT calculations at the computational cost of standard semiempirical methods.     

Energetics of dioxygen binding into graphene patches with various sizes and shapes

Density functional theory (DFT) calculations were employed to investigate the electronic properties of an H-atom terminated graphene patch (hydrographene) smaller than a rhombic C96H26 structure with zigzag edges. Depending on shapes and sizes of hydrographenes, some hydrographenes have the triplet ground state where unpaired electrons are localized on their zigzag edges. The stability of the triplet spin state is diminished, decreasing the hydrographene sizes. The existence of the localized spin densities allows triplet dioxgen to bind into a hydrographene. According to the DFT calculations, the energetics of the dioxygen bindings is negatively influenced by downsizing hydrographenes, as well as depends on their shapes. The size-and shape-dependences of the dioxygen bindings reflect from the stability of the triplet state of a hydrographene, because its localized unpaired electrons can be utilized to be attached to an unpaired electron of triplet dioxygen.     

Highly efficient implementation of pseudospectral time‐dependent density‐functional theory for the calculation of excitation energies of large molecules

We have developed and implemented pseudospectral time‐dependent density‐functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm–Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time‐dependent density‐functional theory with full linear response (PS‐FLR‐TDDFT) and within the Tamm–Dancoff approximation (PS‐TDA‐TDDFT) for G2 set molecules using B3LYP/6‐31G*^* show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS‐FLR‐TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS‐FLR‐TDDFT and best estimations demonstrate that the accuracy of both PS‐FLR‐TDDFT and PS‐TDA‐TDDFT. Calculations for a set of medium‐sized molecules, including C_n fullerenes and nanotubes, using the B3LYP functional and 6‐31G^** basis set show PS‐TDA‐TDDFT provides 19‐ to 34‐fold speedups for C_n fullerenes with 450–1470 basis functions, 11‐ to 32‐fold speedups for nanotubes with 660–3180 basis functions, and 9‐ to 16‐fold speedups for organic molecules with 540–1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46‐residue crambin protein, fullerenes up to C₅₄₀ and nanotubes up to 14×(6,6), using the B3LYP functional and 6‐31G^** basis set with up to 8100 basis functions show that PS‐FLR‐TDDFT CPU time scales as N^2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc.     

反式和顺式HOOOH的电子光谱的理论研究

用密度泛函方法(DFT)和全活化空间自洽场方法(CASSCF)以及耦合簇理论(CCSD)优化了反式和顺式HOOOH的平衡几何构型, 用DFT计算了HOOOH顺反异构化反应的势能曲线和谐振动频率. 用含时密度泛函理论(TD-DFT)和二阶全活化空间微扰理论(CASPT2)计算了反式和顺式HOOOH垂直激发能. 计算结果表明: (1)反式异构体比顺式异构体稳定; (2)两种稳定构型的异构化反应有两种路径; (3)对于垂直跃迁能最低的单态和叁态, 反式的垂直跃迁能比顺式的低; (4)在单激发态中, CASPT2方法预测的顺式HOOOH寿命最长的激发态为21A′′, 其跃迁能是167.43 nm, 寿命为 1.44×10−5 s; 反式HOOOH寿命最长的激发态为21A, 其跃迁能是165.52 nm, 寿命为 2.07×10−5 s.     

On the Influence of Higher Excited States on the ISC Quantum Yield of Octa-aL-alkyloxy-substituted Zn-Phthalocyanine Molecules Studied by Nonlinear Absorption

Abstract— Octa-aL-alkyloxy-substituted Zn-phthalocyanines are an interesting class of far red-absorbing photosensitizers. The chemical structure, the calculated steric conformation, the observed linear optical properties and an anomalous luminescence from a higher than S, excited state are reported. To study the optical properties of higher excited states and their occupation dynamics up to delay times of 15 ns we have carried out measurements of transient absorption spectra after 14 ps pulsed, resonant B-band and Q-band excitation. From these measurements the excited state singlet-singlet and triplet-triplet spectra as well as the intersystem crossing (ISC) quantum yields are obtained. The main result is an excitation wavelength-dependent ISC quantum yield that can be explained by an additional ISC channel between higher excited singlet and triplet states. The large rate of this channel is justified by the resonance between higher triplet states, observed in the triplet-triplet spectrum and the B, absorption band. Using kinetic model calculations, a lifetime of the higher excited singlet state of some picoseconds is predicted and the influence of a two-step absorption process on the population density of this higher excited singlet state is discussed.