Time-dependent density-functional theory in the projector augmented-wave method

We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born-Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method.     

Resonance Raman de-enhancement caused by excited state mixed valence

Resonance Raman and absorption spectra of 9,10-bis(2-tert-butyl-2,3-diazabicyclo[2.2.2]oct-3-yl)-anthracene (2) are measured and analyzed. The contribution of the individual vibrational normal modes to the reorganization energy is investigated. Excited-state mixed valence in this system is analyzed using density functional theory electronic structure calculations. The resonance Raman excitation profiles exhibit a resonance de-enhancement effect around 20 725 cm-1, but a corresponding feature is not observed in the absorption spectrum. This unusual observation is attributed to the presence of a dipole-forbidden, vibronically allowed component of the split mixed valence excited state. The de-enhancement dip is calculated quantitatively and explained in terms of the real and imaginary components of the polarizabilities of the two overlapping excited states.     

Calculation of excited-state properties using general coupled-cluster and configuration-interaction models

Using string-based algorithms excitation energies and analytic first derivatives for excited states have been implemented for general coupled-cluster (CC) models within CC linear-response (LR) theory which is equivalent to the equation-of-motion (EOM) CC approach for these quantities. Transition moments between the ground and excited states are also considered in the framework of linear-response theory. The presented procedures are applicable to both single-reference-type and multireference-type CC wave functions independently of the excitation manifold constituting the cluster operator and the space in which the effective Hamiltonian is diagonalized. The performance of different LR-CC/EOM-CC and configuration-interaction approaches for excited states is compared. The effect of higher excitations on excited-state properties is demonstrated in benchmark calculations for NH(2) and NH(3). As a first application, the stationary points of the S(1) surface of acetylene are characterized by high-accuracy calculations.     

Theory and method for calculating resonance Raman scattering from resonance polarizability derivatives

We present a method to calculate both normal Raman-scattering (NRS) and resonance Raman-scattering (RRS) spectra from the geometrical derivatives of the frequency-dependent polarizability. In the RRS case, the polarizability derivatives are calculated from resonance polarizabilities by including a finite lifetime of the electronic excited states using time-dependent density-functional theory. The method is a short-time approximation to the Kramers, Heisenberg, and Dirac formalism. It is similar to the simple excited-state gradient approximation method if only one electronic excited state is important, however, it is not restricted to only one electronic excited state. Since the method can be applied to both NRS and RRS, it can be used to obtain complete Raman excitation profiles. To test the method we present the results for the S2 state of uracil and the S4, S3, and S2 states of pyrene. As expected, the results are almost identical to the results obtained from the excited-state gradient approximation method. Comparing with the experimental results, we find in general quite good agreement which enables an assignment of the experimental bands to bands in the calculated spectrum. For uracil the inclusion of explicit waters in the calculations was found to be necessary to match the solution spectra. The calculated resonance enhancements are on the order of 10(4)-10(6), which is in agreement with experimental findings. For pyrene the method is also able to distinguish between the three different electronic states for which experimental data are available. The neglect of anharmonicity and solvent effects in the calculations leads to some discrepancy between theory and experiment.     

Theoretical investigation of the energies and geometries of photoexcited uranyl(VI) ion: a comparison between wave-function theory and density functional theory

In order to assess the accuracy of wave-function and density functional theory (DFT) based methods for excited states of the uranyl(VI) UO2(2+) molecule excitation energies and geometries of states originating from excitation from the sigma(u), sigma(g), pi(u), and pi(g) orbitals to the nonbonding 5f(delta) and 5f(phi) have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCFCASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFTMRCI method. Excellent agreement between all nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFTMRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied sigma(u) orbital are symmetric while that arising from excitations out of the pi(u) orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.     

State-selective optimization of local excited electronic states in extended systems

Standard implementations of time-dependent density-functional theory (TDDFT) for the calculation of excitation energies give access to a number of the lowest-lying electronic excitations of a molecule under study. For extended systems, this can become cumbersome if a particular excited state is sought-after because many electronic transitions may be present. This often means that even for systems of moderate size, a multitude of excited states needs to be calculated to cover a certain energy range. Here, we present an algorithm for the selective determination of predefined excited electronic states in an extended system. A guess transition density in terms of orbital transitions has to be provided for the excitation that shall be optimized. The approach employs root-homing techniques together with iterative subspace diagonalization methods to optimize the electronic transition. We illustrate the advantages of this method for solvated molecules, core-excitations of metal complexes, and adsorbates at cluster surfaces. In particular, we study the local π→π(?) excitation of a pyridine molecule adsorbed at a silver cluster. It is shown that the method works very efficiently even for high-lying excited states. We demonstrate that the assumption of a single, well-defined local excitation is, in general, not justified for extended systems, which can lead to root-switching during optimization. In those cases, the method can give important information about the spectral distribution of the orbital transition employed as a guess.     

A theoretical investigation of the photo-induced intramolecular charge transfer excitation of cuprous (I) bis-phenanthroline by density functional theory

This work reported an investigation on the excited state and electronic transfer excitation of cuprous (I) bis-phenanthrouline complex by density functional theory. The intramolecular charge transfer from central metal to ligand (MLCT) during the excitation was observed. The transfer direction and degree were discussed on the basis of analyzing the Mulliken charge. The structural distortion caused by the charge transfer in the excited state was confirmed. The excited state was found having the characters similar with Cu(II) complex both in electronic and geometrical properties. The large structural distortion found between ground state and excited state could lead to a decrease in the lifetime of excited state as well as a non-radiative decay. The excitation energies and oscillator strengths of cuprous (I) bis-phenanthrouline were derived using time-dependent density functional method. The values of excitation energies are good agreement with the results of the experimental measuring.     

Excited state properties, fluorescence energies, and lifetime of a poly(fluorene-pyridine) copolymer, based on TD-DFT investigation

The structural and electronic properties of the fluorene-pyridine copolymer (FPy)(n), (n = 1-4) were investigated theoretically by means of quantum mechanical calculations based on density functional theory (DFT) and time-dependent DFT (TD-DFT) using the B3LYP functional. Geometry optimizations of these oligomers were performed for the ground state and the lowest excited state. It was found that (FPy)(n) is nonplanar in its ground state, whereas a more pronounced trend toward planarity is observed in the S(1) state. Absorption and fluorescence energies have been extrapolated to infinite chain length making use of their good linearity with respect to 1/n. An extrapolated value of 2.64 eV is obtained for vertical excitation energy. The S(1)<--S(0) electronic excitation is characterized as a highest occupied molecular orbital to lowest unoccupied molecular orbital transition and is dominating in terms of oscillator strength. Fluorescence energies and radiative lifetime were calculated as well. The obtained results indicate that the fluorescence energy and radiative lifetime of (FPy)(n) are 2.16 eV and 0.38 ns, respectively. The decrease of fluorescence energy and radiative lifetime with the increase in the chain length is discussed.     

Charge transfer excitations in cofacial fullerene-porphyrin complexes

Porphyrin and fullerene donor-acceptor complexes have been extensively studied for their photo-induced charge transfer characteristics. We present the electronic structure of ground states and a few charge transfer excited states of four cofacial porphyrin-fullerene molecular constructs studied using density functional theory at the all-electron level using large polarized basis sets. The donors are base and Zn-tetraphenyl porphyrins and the acceptor molecules are C(60) and C(70). The complexes reported here are non-bonded with a face-to-face distance between the porphyrin and the fullerene of 2.7 to 3.0 A?. The energies of the low lying excited states including charge transfer states calculated using our recent excited state method are in good agreement with available experimental values. We find that replacing C(60) by C(70) in a given dyad may increase the lowest charge transfer excitation energy by about 0.27 eV. Variation of donor in these complexes has marginal effect on the lowest charge transfer excitation energy. The interfacial dipole moments and lowest charge transfer states are studied as a function of face-to-face distance.     

Theory for the optical properties of small Hg n clusters

The static and dynamical polarizabilities of the Hg-dimer are calculated by using a Hubbard Hamiltonian to describe the electronic structure. The Hamiltonian is diagonalized exactly within a subspace of second-quantized electronic states from which only multiply ionized atomic configurations have been excluded. With this approximation we can describe the most important electronic transitions including the effect of charge fluctuations. We analyze the polarizability as a function of the intraatomic Coulomb interaction which represents the repulsion between electrons. We obtain that this interaction results in strong electronic correlations in the excited states and increases the first excitation energy of the dimer by 0.8 eV in comparison to a calculation which neglects correlations, resulting in a better agreement with the experiment.     

Application of an efficient multireference approach to free-base porphin and metalloporphyrins: ground, excited, and positive ion states

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method is applied to determine the geometries of the ground state of free-base porphin and its metal derivatives, magnesium and zinc porphyrins. The vertical excitation energies and ionization potentials are computed at these optimized geometries using an IVO-based version of multireference Mo?ller-Plesset (IVO-MRMP) perturbation theory. The geometries and excitation energies obtained from the IVO-CASCI and IVO-MRMP methods agree well with experiment and with other correlated many-body methods. We also provide the ground state vibrational frequencies for free-base porphin and Mg-porphyrin. All frequencies are real in contrast to self-consistent field treatments which yield an imaginary frequency. Ground state normal mode frequencies (scaled) of free-base porphin and magnesium porphyrin from IVO-CASCI and complete active space self-consistent field methods are quite similar and are consistent with Becke-Slater-Hartree-Fock exchange and Lee-Yang-Parr correlation density functional theory calculations and with experiment. In addition, geometries are determined for low-lying excited state triplets and for positive ion states of the molecules. To our knowledge, no prior experimental and theoretical data are available for these excited state geometries of magnesium and zinc porphyrins. Given that the IVO-CASCI and IVO-MRMP computed geometries and excitation energies agree favorably with experiment and with available theoretical data, our predicted excited state geometries should be equally accurate.     

Ab initio calculation of the electronic absorption of functionalized octahedral silsesquioxanes via time-dependent density functional theory with range-separated hybrid functionals

Recent advances in the ability to functionalize octahedral silsesquioxanes with different photoactive ligands, and thereby tune their optical properties, suggest that these molecules may serve as potential building blocks of light-harvesting, photovoltaic, and photonic devices. In this paper we report extensive ab initio calculations of the excitation energies underlying the absorption spectra of these systems. The calculations are based on density functional theory for the ground electronic state and time-dependent density functional theory for the excited electronic states. The ability of the commonly used B3LYP functional to reproduce the experimentally observed absorption excitation energies is compared to that of recently developed range-separated hybrid functionals. The importance of pairing the range-separated hybrid functionals with basis sets that include diffuse and polarization basis functions is demonstrated in the case of vinyl-functionalized silsesquioxanes. Absorptive excitation energies are then calculated and compared with experiment for octahedral silsesquioxanes functionalized with larger ligands. The tunability of optical properties is demonstrated by considering the effect on the excitation energies of functionalizing the ligands with electron-donating or -withdrawing groups.     

Radical ions and radicals in electron-irradiated acrylates and N-isopropylacrylamide: a quantum chemical study

The semiempirical quantum chemical methods MNDO, AM1 and PM3 were used to investigate the performance of the single excited configuration interaction (SCI) approximation for calculating low energy excitation energies of open-shell systems. Systematic calculations were done for eight radicals formed by reactions of H√, OH√ and e⁻_aq with various acrylates and N-isopropylacrylamide. The calculated electronic spectra show a reasonable correlation with experimental data for both neutral radicals and radical ions. The AM1 as well as the PM3 formalism can be successfully applied to calculate the low energy excited states of these types of open shell systems. The best correlation between experimental and calculated excitation energies was obtained using the PM3 method (correlation coefficient 0.96, overall average error 0.16 eV).     

On low‐lying excited states of extended nanographenes

Low‐lying excited states of planarly extended nanographenes are investigated using the long‐range corrected (LC) density functional theory (DFT) and the spin‐flip (SF) time‐dependent density functional theory (TDDFT) by exploring the long‐range exchange and double‐excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long‐range exchange interaction significantly improves the C C bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long‐range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long‐range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long‐range exchange effects, the SF‐TDDFT calculations show that the double‐excitation correlation effects are negligible in the low‐lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long‐range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP–EA values. © 2017 Wiley Periodicals, Inc.     

Quantum chemical modeling of photoadsorption properties of the nitrogen-vacancy point defect in diamond

Quantum chemical calculations of geometric and electronic structure and vertical transition energies for several low-lying excited states of the neutral and negatively charged nitrogen-vacancy point defect in diamond (NV(0) and NV(-)) have been performed employing various theoretical methods and basis sets and using finite model NC(n)H(m) clusters. Unpaired electrons in the ground doublet state of NV(0) and triplet state of NV(-) are found to be localized mainly on three carbon atoms around the vacancy and the electronic density on the nitrogen and rest of C atoms is only weakly disturbed. The lowest excited states involve different electronic distributions on molecular orbitals localized close to the vacancy and their wave functions exhibit a strong multireference character with significant contributions from diffuse functions. CASSCF calculations underestimate excitation energies for the anionic defect and overestimate those for the neutral system. The inclusion of dynamic electronic correlation at the CASPT2 level leads to a reasonable agreement (within 0.25 eV) of the calculated transition energy to the lowest excited state with experiment for both systems. Several excited states for NV(-) are found in the energy range of 2-3 eV, but only for the 1(3)E and 5(3)E states the excitation probabilities from the ground state are significant, with the first absorption band calculated at approximately 1.9 eV and the second lying 0.8-1 eV higher in energy than the first one. For NV(0), we predict the following order of electronic states: 1(2)E (0.0), 1(2)A(2) (approximately 2.4 eV), 2(2)E (2.7-2.8 eV), 1(2)A(1), 3(2)E (approximately 3.2 eV and higher).     

Influence of geometry relaxation on the energies of the S1 and S2 states of violaxanthin, zeaxanthin, and lutein

Precise knowledge of the excitation energies of the lowest excited states S(1) and S(2) of the carotenoids violaxanthin, lutein, and zeaxanthin is a prerequisite for a fundamental understanding of their role in light harvesting and photoprotection during photosynthesis. By means of density functional theory (DFT) and time-dependent DFT (TDDFT), the electronic and structural properties of the ground and first and second excited states are studied in detail. According to our calculations, all-s-cis-zeaxanthin and s-cis-lutein conformers possess lower total ground-state energies than the corresponding s-trans conformers. Thus, only s-cis isomers are probably physiologically relevant. Furthermore, the influence of geometric relaxation on the energies of the ground state and S(1) and S(2) states has been studied in detail. It is demonstrated that the energies of these states change significantly if the carotenoid adopts the equilibrium geometry of the S(1) state. Considering these energetic effects in the interpretation of S(1) excitation energies obtained from fluorescence and transient absorption spectroscopy shifts the S(1) excitation energies about 0.2 eV to higher energy above the excitation energy of the chlorophyll a.     

The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculations of excitation energies

In the present work we have studied the accuracy of excitation energies calculated from spin-flip transitions with a formulation of time-dependent density functional theory based on a noncollinear exchange-correlation potential proposed in a previous study. We compared the doublet-doublet excitation energies from spin-flip transitions and ordinary transitions, calculated the multiplets splitting of some atoms, the singlet-triplet gaps of some diradicals, the energies of excited quartet states with a doublet ground state. In addition, we attempted to calculate transition energies with excited states as reference. We compared the triplet excitation energies and singlet-triplet separations of the excited state from spin-flip and ordinary transitions. As an application, we show that using excited quartet state as reference can help us fully resolve excited states spin multiplets. In total the obtained excitation energies calculated from spin-flip transitions agree quite well with other theoretical results or experimental data.     

A CASSCF/CASPT2 study on the low-lying excited states of HSiCN, HSiNC and their ions

Equilibrium geometries of low-lying electronic states of cyanosilylene (HSiCN), isocyanosilylene (HSiNC), and their ions have been investigated using the complete active space self-consistent field (CASSCF) approach. The harmonic vibrational frequencies on the optimized geometries were calculated using the multiconfiguration linear response (MCLR) method. Taking the further correlation effects into account, the complete active space perturbation theory of second-order (CASPT2) was carried out for the energetic correction. The CASPT2 calculations have been performed to obtain the vertical excitation energies of selected low-lying excited states of HSiCN and HSiNC. Computed results show that the singlet-triplet splittings are calculated to be 0.99 and 1.30 eV for HSiCN and HSiNC, respectively. The vertical excitation energies of the lowest singlet and triplet excited states in HSiCN are lower than those in HSiNC. The first vertical ionization energy of HSiCN (10.04 eV) is higher than that of HSiNC (9.97 eV). The ground-state adiabatic electron affinities are found to be rather high, and the value of HSiCN (1.85 eV) higher than that of HSiNC (1.52 eV). The existences of dipole-bound excited negative ion states have been discovered within HSiCN and HSiNC.