Theoretical study of singlet and triplet excitation energies in oligothiophenes

We have analyzed singlet and triplet excitation energies in oligothiophenes (up to five rings) using time-dependent density-functional theory (TD-DFT) with different exchange-correlation functionals and compared them with results from the approximate coupled-cluster singles and doubles model (CC2) and experimental data. The excitation energies have been calculated in geometries obtained by TD-DFT optimization of the lowest excited singlet state and in the ground-state geometries of the neutral and anionic systems. TD-DFT methods underestimate photoluminescence energies but the energy difference between singlet and triplet states shows trends with the chain-length similar to CC2. We find that the second triplet excited state is below the first singlet excited state for long oligomers in contrast with the previous assignment of Rentsch et al. (Phys.Chem. Chem. Phys. 1999, 1, 1707). Their photodetachment photoelectron spectroscopy measurements are better described by considering higher triplet excited states.     

Reduction of the virtual space for coupled-cluster excitation energies of large molecules and embedded systems

We investigate how the reduction of the virtual space affects coupled-cluster excitation energies at the approximate singles and doubles coupled-cluster level (CC2). In this reduced-virtual-space (RVS) approach, all virtual orbitals above a certain energy threshold are omitted in the correlation calculation. The effects of the RVS approach are assessed by calculations on the two lowest excitation energies of 11 biochromophores using different sizes of the virtual space. Our set of biochromophores consists of common model systems for the chromophores of the photoactive yellow protein, the green fluorescent protein, and rhodopsin. The RVS calculations show that most of the high-lying virtual orbitals can be neglected without significantly affecting the accuracy of the obtained excitation energies. Omitting all virtual orbitals above 50 eV in the correlation calculation introduces errors in the excitation energies that are smaller than 0.1 eV. By using a RVS energy threshold of 50 eV, the CC2 calculations using triple-ζ basis sets (TZVP) on protonated Schiff base retinal are accelerated by a factor of 6. We demonstrate the applicability of the RVS approach by performing CC2/TZVP calculations on the lowest singlet excitation energy of a rhodopsin model consisting of 165 atoms using RVS thresholds between 20 eV and 120 eV. The calculations on the rhodopsin model show that the RVS errors determined in the gas-phase are a very good approximation to the RVS errors in the protein environment. The RVS approach thus renders purely quantum mechanical treatments of chromophores in protein environments feasible and offers an ab initio alternative to quantum mechanics/molecular mechanics separation schemes.     

Benchmarking the performance of spin-component scaled CC2 in ground and electronically excited states

A generalization of the spin-component scaling and scaled opposite-spin modifications of second-order M?ller-Plesset perturbation theory to the approximate coupled-cluster singles-and-doubles model CC2 (termed SCS-CC2 and SOS-CC2) is discussed and a preliminary implementation of ground and excited state energies and analytic gradients is reported. The computational results for bond distances, harmonic frequencies, adiabatic and 0-0 excitation energies are compared with experimental results to benchmark their performance. It is found that both variants of the spin-scaling increase the robustness of CC2 against strong correlation effects and lead for this method even to somewhat larger improvements than those observed for second-order M?ller-Plesset perturbation theory. The spin-component scaling also enhances systematically the accuracy of CC2 for 0-0 excitation energies for pi --> pi* and n --> pi* transitions, if geometries are determined at the same level.     

Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3

A benchmark set of 28 medium-sized organic molecules is assembled that covers the most important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic hydrocarbons, heterocycles, carbonyl compounds, and nucleobases. Vertical excitation energies and one-electron properties are computed for the valence excited states of these molecules using both multiconfigurational second-order perturbation theory, CASPT2, and a hierarchy of coupled cluster methods, CC2, CCSD, and CC3. The calculations are done at identical geometries (MP26-31G*) and with the same basis set (TZVP). In most cases, the CC3 results are very close to the CASPT2 results, whereas there are larger deviations with CC2 and CCSD, especially in singlet excited states that are not dominated by single excitations. Statistical evaluations of the calculated vertical excitation energies for 223 states are presented and discussed in order to assess the relative merits of the applied methods. CC2 reproduces the CC3 reference data for the singlets better than CCSD. On the basis of the current computational results and an extensive survey of the literature, we propose best estimates for the energies of 104 singlet and 63 triplet excited states.     

Ab initio calculation of the vibrational and electronic spectra of trans- and cis-azobenzene

We report accurate geometries and harmonic force fields for trans- and cis-azobenzene determined by second-order M?ller-Plesset perturbation theory. For the trans isomer, the planar structure with C(2h) symmetry, found in a recent gas electron diffraction experiment, is verified. The calculated vibrational spectra are compared with experimental data and density functional calculations. Important vibrational frequencies are localized and discussed. For both isomers, we report UV spectra calculated using the second-order approximate coupled-cluster singles-and-doubles model CC2 with accurate basis sets. Vertical excitation energies and oscillator strengths have been determined for the lowest singlet n(pi)* and (pi)(pi)* transitions. The results are compared with the available experimental data and second-order polarization propagator (SOPPA) and density functional (DFT) calculations. For both isomers, the CC2 results for the excitation energies into the S(1) and S(2) states agree within 0.1 eV with experimental gas-phase measurements.     

Computational studies of photophysical properties of porphin, tetraphenylporphyrin and tetrabenzoporphyrin

The molecular photonics of porphyrins are studied using a combination of first-principle and semi-empirical calculations. The applicability of the approach is demonstrated by calculations on free-base porphyrin, tetraphenylporphyrin, and tetrabenzoporphyrin. The method uses excitation energies and oscillator strengths calculated at the linear-response time-dependent density functional theory (TDDFT) or the corresponding values calculated at the linear-response approximate second-order coupled-cluster (CC2) levels. The lowest singlet excitation energies obtained in the TDDFT and CC2 calculations are 0.0-0.28 eV and 0.18-0.47 eV larger than the experimental values, respectively. The excitation energies for the first triplet state calculated at the TDDFT level are in excellent agreement with experiment, whereas the corresponding CC2 values have larger deviations from experiment of 0.420.66 eV. The matrix elements of the spin-orbit and non-adiabatic coupling operators have been calculated at the semi-empirical intermediate neglect of differential overlap (INDO) level using a spectroscopic parameterization. The calculations yield rate constants for internal conversion and intersystem crossing processes as well as quantum yields for fluorescence and phosphorescence. The main mechanism for the quenching of fluorescence in tetraphenylporphyrin and tetrabenzoporphyrin is the internal conversion, whereas for free-base porphyrin both the internal conversion and the intersystem crossing processes reduce the fluorescence intensity. The phosphorescence is quenched by a fast internal conversion from the triplet to the ground state.     

Theoretical investigation of the excited states of coumarin dyes for dye-sensitized solar cells

Using time-dependent density functional theory (TD-DFT), configuration interaction single (CIS) method, and approximate coupled cluster singles and doubles (CC2) method, we investigated the absorption spectra of coumarin derivative dyes (C343, NKX-2388, NKX-2311, NKX-2586, and NKX-2677), which have been synthesized for efficient dye-sensitized solar cells. The CC2 calculations are found in good agreement with the experimental results except for the smallest coumarin dye (C343). TD-DFT underestimates the vertical excitation energy of the larger coumarin dyes (NKX-2586 and -2677). Solvents (methanol) are found to induce a red shift of the vertical excitation energies, and their effects on the molecular geometry and the electronic structure are examined in detail. The deprotonated form of coumarin is also investigated, where a blue shift of the vertical excitation energies is observed.     

Generalization of coupled-cluster response theory to multireference expansion spaces: application of the coupled-cluster singles and doubles effective Hamiltonian

Employing separate cluster ansatz in time-independent and time-dependent wave-operators, coupled-cluster (CC) response theory is generalized to multireference (MR) expansion spaces. For state energies, this corresponds to the MR secular problem with an arbitrary similarity-transformed effective Hamiltonian, H˜=Ω⁻¹ HΩ. The effective Hamiltonian can be generated via size-extensive CC methods. Thus the states in MR linear response theory (MRLRT) maintain the usual CC core-extensive properties. We have used the Gelfand unitary group basis of the spin-adapted configurations to construct the matrix of H˜ in the MR excitation space. As a preliminary application, the CC singles and doubles effective Hamiltonian is applied to excitation and photoionization energies of the CH⁺ and N₂ molecules, and is compared with experimental results and results from other numerical procedures including conventional CC linear response theory (CC-LRT), MR and full configuration interaction (MRCI and FCI) methods. The numerical results indicate that MRLRT reproduces valence and external excited states quantitatively, combining the best features of CC-LRT and MRCI. Received: 2 July 1998 / Accepted: 28 August 1998 / Published online: 11 November 1998     

The Excitation Spectra of Naphthalene Dimers: Frenkel and Charge‐transfer Excitons

Vertical electronic excitation energies have been calculated at the second‐order approximate coupled‐cluster (CC2) level for a series of dimeric naphthalene systems. The calculated excitation energies are compared with values obtained for a single naphthalene molecule and provide information about the coupling between the naphthalene moieties in the dimers. The calculations show that the coupling between the naphthalenes depends on the distance and the energy of the exciton. At long distances and high energies the excitons on the two naphthalenes are strongly coupled, whereas the excitation energies of the few lowest states are almost unaffected by the presence of the neighboring molecules. We have also analyzed the composition of the dimeric states that consist of the individual monomer states, to investigate the charge‐transfer (CT) and the Frenkel character of the excitons. Our results indicate that the CT exciton exists at short distances, and that its population drops as the distance between the two naphthalene increases.     

Quantum-chemical investigation of the structures and electronic spectra of the nucleic acid bases at the coupled cluster CC2 level

We study the ground-state structures and singlet- and triplet-excited states of the nucleic acid bases by applying the coupled cluster model CC2 in combination with a resolution-of-the-identity approximation for electron interaction integrals. Both basis set effects and the influence of dynamic electron correlation on the molecular structures are elucidated; the latter by comparing CC2 with Hartree-Fock and M?ller-Plesset perturbation theory to second order. Furthermore, we investigate basis set and electron correlation effects on the vertical excitation energies and compare our highest-level results with experiment and other theoretical approaches. It is shown that small basis sets are insufficient for obtaining accurate results for excited states of these molecules and that the CC2 approach to dynamic electron correlation is a reliable and efficient tool for electronic structure calculations on medium-sized molecules.     

Coupled cluster methods including triple excitations for excited states of radicals

We report an extension of the coupled cluster iterative-triples model, CC3, to excited states of open-shell molecules, including radicals. We define the method for both spin-unrestricted Hartree-Fock (UHF) and spin-restricted open-shell Hartree-Fock (ROHF) reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most O(N(7)) computational steps and avoids storage of the triple-excitation amplitudes for both the ground- and excited-state calculations. The excitation-energy program makes use of a Lowdin projection formalism (comparable to that of earlier implementations) that allows computational reduction of the Davidson algorithm to only the single- and double-excitation space, but limits the calculation to only one excited state at a time. However, a root-following algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence (2)B(1) state of the allyl radical, low-lying states of the CH and CO(+) diatomics, and the nitromethyl radical show substantial improvement over ROHF- and UHF-based CCSD excitation energies for states with strong double-excitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the (2)Sigma(+) state of CH, significant errors of more than 0.4 eV remain.     

Coupled-cluster studies of the electronic excitation spectra of silanes

The electronic excitation spectra of unsubstituted linear silanes (n-Si(m)H(2m+2), m = 1-6), cyclopentasilane (c-Si5H10), and neopentasilane (neo-Si5H12) have been studied at the coupled-cluster approximate singles and doubles (CC2) level using Dunning's quadruple-zeta basis sets augmented with diffuse functions (aug-cc-pVQZ). Comparisons with measured ultraviolet spectra for Si2H6 and n-Si3H8 show that CC2 calculations using these basis sets yield excitation energies in good agreement with experiment. The calculated excitation thresholds for Si2H6 and n-Si3H8 of 7.61 and 6.68 eV are only 0.05 eV larger than the gas-phase values of 7.56 and 6.63 eV, respectively. For n-Si4H10, n-Si5H12, and neo-Si5H12, the calculated excitation thresholds of 6.51, 6.14, and 6.87 eV for the lowest dipole-allowed transitions are about 0.4 eV larger than the corresponding liquid-phase data of 6.05, 5.77, and 6.53 eV; the discrepancy can mainly be attributed to solvent effects. The obtained excitation thresholds for n-Si6H14 is 5.85 eV, whereas no experimental data are available for its optical gap. Calculations using the Karlsruhe triple-zeta valence basis sets augmented with single and double sets of polarization functions show that very large basis sets augmented with diffuse functions are needed for obtaining accurate excitation energies. The optical gaps for silanes obtained using the triple-zeta polarization basis sets were found to be 0.4 and 0.2 eV larger than those obtained using Dunning's quadruple-zeta basis sets. Excitation thresholds calculated at density functional theory levels using generalized gradient approximation are 0.7-1.0 eV smaller than the experimental values and by employing hybrid functionals they are 0.3-0.4 eV below the experimental thresholds. By adding the present basis-set correction and environmental effects to the previously calculated CC2 value for the excitation threshold of the Si29H36 silicon nanocluster, the extrapolated absorption threshold is 4.0 eV as compared to the recently reported experimental value of 3.7 eV.     

Theoretical study of the electronic structure of MCH(2)(+)(M=Fe,Co,Ni)

State of the art coupled cluster (CC) methods are applied to accurately characterize the ground state electronic structure and photoelectron spectra of transition metal carbene ions MCH(2) (+) (M=Fe, Co, and Ni). The geometries and energies of the lowest energy quartet, triplet, and doublet electronic states as well as several low-lying vertical excitation energies of FeCH(2) (+), CoCH(2) (+), and NiCH(2) (+) are reported. The excitation energies are computed using the equation-of-motion CC and for states of different symmetries, by the energy differences of single reference ground and excited states (Delta-CC). The latter employ several reference states; the unrestricted Hartree-Fock, restricted open shell Hartree-Fock, and unrestricted Kohn-Sham. We conclude that the (2)A(1) electronic ground state of NiCH(2) (+) is separated by about 30.0 kJ/mol from the next highest state, and the lowest (4)B(1) and (4)B(2) states of FeCH(2) (+) as well as the (3)A(2) and (3)A(1) states of CoCH(2) (+) are nearly degenerate. The presence of metal-pi*(MCH(2)) charge transfer states with significant oscillator strengths in the visible/near-UV energy domain of the theoretical spectra of FeCH(2) (+) and CoCH(2) (+) are at the origin of the photofragmentation of these compounds observed after irradiation between 310 and 360 nm.     

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.     

Excited States of Xanthene Analogues: Photofragmentation and Calculations by CC2 and Time‐Dependent Density Functional Theory

Action spectroscopy has emerged as an analytical tool to probe excited states in the gas phase. Although comparison of gas‐phase absorption properties with quantum‐chemical calculations is, in principle, straightforward, popular methods often fail to describe many molecules of interest—such as xanthene analogues. We, therefore, face their nano‐ and picosecond laser‐induced photofragmentation with excited‐state computations by using the CC2 method and time‐dependent density functional theory (TDDFT). Whereas the extracted absorption maxima agree with CC2 predictions, the TDDFT excitation energies are blueshifted. Lowering the amount of Hartree–Fock exchange in the DFT functional can reduce this shift but at the cost of changing the nature of the excited state. Additional bandwidth observed in the photofragmentation spectra is rationalized in terms of multiphoton processes. Observed fragmentation from higher‐lying excited states conforms to intense excited‐to‐excited state transitions calculated with CC2. The CC2 method is thus suitable for the comparison with photofragmentation in xanthene analogues.     

Ab initio description of photoabsorption and electron transfer in a doubly-linked porphyrin-fullerene dyad

Structure, photoabsorption and excited states of two representative conformations obtained from molecular dynamics (MD) simulations of a doubly-linked porphyrin-fullerene dyad DHD6ee are studied by using both DFT and wavefunction based methods. Charge transfer from the donor (porphyrin) to the acceptor (fullerene) and the relaxation of the excited state are of special interest. The results obtained with LDA, GGA, and hybrid functionals (SVWN, PBE, and B3LYP, respectively) are analyzed with emphasis on the performance of used functionals as well as from the point of view of their comparison with wavefunction based methods (CCS, CIS(D), and CC2). Characteristics of the MD structures are retained in DFT optimization. The relative orientation of porphyrin and fullerene is significantly influencing the MO energies, the charge transfer (CT) in the ground state of the dyad and the excitation of ground state CT complex (g-CTC). At the same time, the excitation to the locally excited state of porphyrin is only little influenced by the orientation or cc distance. TD-DFT underestimates the excitation energy of the CT state, however for some cases (with relatively short donor-acceptor separations), the use of a hybrid functional like B3LYP alleviates the problem. Wavefunction based methods and CC2 in particular appear to overestimate the CT excitation energies but the inclusion of proper solvation models can significantly improve the results.     

Theoretical study of the electronic gas-phase spectrum of glycine, alanine, and related amines and carboxylic acids

A theoretical study on the origin of the common electronic excitations in amino acids is presented, focusing on the excited states of glycine, alanine and the related substructures formic acid, acetic acid, propionic acid, ammonia, methylamine, and ethylamine. Special attention is given to the valence excitation from the nonbonding lone-pair on the carboxylic oxygen atom to the antibonding pi-orbital (n(O) --> pi*(CO)) and the first Rydberg excitation from the nonbonding lone-pair on the nitrogen atom (n(N) --> 3s). From extensive calculations on formic acid and methylamine, different basis sets and electron correlation treatments are benchmarked using a hierarchy of coupled cluster (CC) methods, consisting of CCS, CC2, CCSD, CCSDR(3), and CC3, in combination with augmented correlation consistent basis sets. The dependence of the excitation energies on the size of the backbone structure in the two groups of molecules is investigated, and 0-0 transition energies for the n(O) --> pi*(CO) and n(N) --> 3s transitions are calculated for the smallest molecules. Excellent agreement with experimental values is found where secure experimental assignments are available. A few outstanding problems in the experimental assignments found in the literature are described for both the carboxylic acids and the amines. Final predictions for vertical excitation energies are given for all molecules, including glycine and alanine where no gas-phase experimental results are available. Finally, calculations on protonated amino acids are presented showing an isolation of the n(O) --> pi*(CO) from higher lying states by as much as 1.9 eV for alanine.     

Coupled‐cluster theory for the polarizable continuum model. III. A response theory for molecules in solution

A coupled‐cluster (CC) response functions theory for molecular solutes described with the framework of the polarizable continuum model (PCM) is presented. The theory is an extension to the dynamical molecular properties of the PCM‐CC analytic derivatives recently proposed for the calculation of static molecular properties (Cammi, Jr Chem Phys 2009, 131, 164104). The theory is presented for linear and quadratic response functions, and the operative expressions of these response functions can accurately account for the nonequilibrium solvation effects. The excitation energies and transition moments of the solvated chromophores have been determined from the linear response functions. Accurate expressions for gradients of excitation energies for the evaluation of the excited state properties have been also discussed. © 2012 Wiley Periodicals, Inc. Int J Quantum Chem, 2012