Calculation Of Vertical Excitation Energies Research Articles

Electronic spectra of oxygen containing polycyclic hydrocarbon cations and the protonated analogues.

The electronic transitions of 9-fluorenone FL(+) and 2,3,6,7-dibenzotropone DBT(+) cations were detected in 6 K neon matrices following a mass-selective deposition. The absorptions at 649.2 and 472.2 nm are assigned to the 2 (2)B1←X̃(2)A2 FL(+) and 2(2)A(')←X̃(2)A(') DBT(+) transitions. Absorption spectra of protonated 9-fluorenone H(+)-FL and 2,3,6,7-dibenzotropone H(+)-DBT have also been measured. Protonation of the oxygenated polycyclic aromatic hydrocarbons is carried out in a hot cathode source via in situ produced protonated ethanol. Vibrationally resolved absorptions commencing at 423.3 nm of H-FL(+) and two band systems of H-DBT(+) with origins at 502.4 and 371.5 nm are assigned to the 2(1)A(')←X̃(1)A(') electronic transition of 9-hydroxy-fluorenyl cation and 1 (1)A←X̃(1)A, 2 (1)A←X̃(1)A of 2,3,6,7-dibenzocycloheptenol cation. The assignments are based on vertical excitation energy calculations with time dependent density functional theory, symmetry adapted cluster configuration interaction, and MS-CASPT2 methods.

Performance of SOPPA-based methods in the calculation of vertical excitation energies and oscillator strengths

We present two new modifications of the second-order polarization propagator approximation (SOPPA), SOPPA(SCS-MP2) and SOPPA(SOS-MP2), which employ either spin-component-scaled or scaled opposite-spin MP2 correlation coefficients instead of the regular MP2 coefficients. The performance of these two methods, the original SOPPA method as well as SOPPA(CCSD) and RPA(D) in the calculation of vertical electronic excitation energies and oscillator strengths is investigated for a large benchmark set of 28 medium-sized molecules with 139 singlet and 71 triplet excited states. The results are compared with the corresponding CC3 and CASPT2 results from the literature for both the TZVP set and the larger and more diffuse aug-cc-pVTZ basis set. In addition, the results with the aug-cc-pVTZ basis set are compared with the theoretical best estimates for this benchmark set. We find that the original SOPPA method gives overall the smallest mean deviations from the reference values and the most consistent results.

A DFT study of the ionization and electron attachment of 2-azido pyridine

A DFT study using B3LYP/6-31G(d,p) level of theory is pursued to investigate the energy and geometry changes of 2-azido pyridine isomers in the S0, D0+, and D0−. In S0, cis-2 azidopyridine is the most stable, followed by cyclic tetrazole and trans isomer is the least stable. In D0+, the cis isomer is the most stable, followed by trans isomer, and tetrazole isomer is the least stable. In the D0− state, the trans form is the most stable, followed by the cis and the tetrazolo form is the least stable. Single point vertical excitation energy calculations of the cis form gave four excited states at 266.4, 239.4, 199.4, and 196.1nm, all having π–π∗ character. For trans isomer, five excited states at, 256.7, 250.3, 229.7, 199.0, 197.0nm all resulting from π–π∗ transitions. For the tetrazole isomer, seven excited states at 269.3, 242.7, 198.0, 187.2, 183.9, 182.1, 178.7nm all resulting from π–π∗ transitions. The geometries of the 3 isomers show noticeable changes in bond lengths, bond angles and dihedral angles, upon ionization and electron attachment. The ionization results in a remarkable variation of the NBO atomic charges as a result of ionization and electron attachment. where electron density of HOMO of the D0+ state is found to be much lower than that of the HOMO of the S0 in the case of ionization. The dipole moment calculations show that tetrazole isomer has the largest polarization in the S0 state, followed by cis isomer and trans isomer is the least polarized. The same pattern is found in the D0+ state. In the D0− state, trans isomer is the highest polarized, followed by the cis, and tetrazole isomer is the least polarized. The rotational constants calculations of cis- isomer show that the cation is elongated along the long in-plane axis and compressed along the two short out-of-plane axes while the anion is compressed along the long in-plane axis, and elongated along the two short out-of plane axes. The cation and anion of trans isomer show similar behavior to the cis isomer. The cation of cyclic tetrazole, is compressed along the long in-plane axis and elongated along the two short out-of-plane axes, while the anion elongates along the 3 mutually perpendicular axes.

Spectroscopy of Nitrophenolates in Vacuo: Effect of Spacer, Configuration, and Microsolvation on the Charge-Transfer Excitation Energy

In a charge-transfer (CT) transition, electron density moves from one end of the molecule (donor) to the other end (acceptor). This type of transition is of paramount importance in nature, for example, in photosynthesis, and it governs the excitation of several protein biochromophores and luminophores such as the oxyluciferin anion that accounts for light emission from fireflies. Both transition energy and oscillator strength are linked to the coupling between the donor and acceptor groups: The weaker the coupling, the smaller the excitation energy. But a weak coupling necessarily also causes a low oscillator strength possibly preventing direct excitation (basically zero probability in the noncoupling case). The coupling is determined by the actual spacer between the two groups, and whether the spacer acts as an insulator or a conductor. However, it can be difficult or even impossible to distinguish the effect of the spacer from that of local solvent molecules that often cause large solvent shifts due to different ground-state and excited-state stabilization. This calls for gas-phase spectroscopy experiments where absorption by the isolated molecule is identified to unequivocally establish the intrinsic molecular properties with no perturbations from a microenvironment. From such insight, the effect of a protein microenvironment on the CT excited state can be deduced. In this Account, we review our results over the last 5 years from mass spectroscopy experiments using specially designed apparatus on several charged donor-acceptor ions that are based on the nitrophenolate moiety and π-extended derivatives, which are textbook examples of donor-acceptor chromophores. The phenolate oxygen is the donor, and the nitro group is the acceptor. The choice of this system is also based on the fact that phenolate is a common structural motif of biochromophores and luminophores, for example, it is a constituent of the oxyluciferin anion. A presentation of the setups used for gas-phase ion spectroscopy in Aarhus is given, and we address issues of whether double bonds or triple bonds best convey electronic coupling between the phenolate oxygen and the nitro group, the significance of separating the donor and acceptor spatially, the influence of cross-conjugation versus linear conjugation, and along this line ortho versus meta versus para configuration, and not least the effect of a single solvent molecule (water, methanol, or acetonitrile). From systematic studies, a clear picture has emerged that has been supported by high-level calculations of electronically excited states. Our work shows that CC2 coupled-cluster calculations of vertical excitation energies are within 0.2 eV of experimental band maxima, and importantly, that the theoretical method is excellent in predicting the relative order of excitation energies of a series of nitrophenolates. Finally, we discuss future challenges such as following the change in absorption as a function of the number of solvent molecules and when gradually approaching the bulk limit.

Influence of Exchange-Correlation Functional in the Calculations of Vertical Excitation Energies of Halogenated Copper Phthalocyanines using Time-Dependent Density Functional Theory (TD-DFT)

The accurate prediction of vertical excitation energies is very important for the development of new materials in the dye and pigment industry. A time-dependent density functional theory (TD-DFT) approach coupled with 22 different exchange-correlation functionals was used for the prediction of vertical excitation energies in the halogenated copper phthalocyanine molecules in order to find the most appropriate functional and to determine the accuracy of the prediction of the absorption wavelength and observed spectral shifts. Among the tested functional, B3LYP functional provides much more accurate vertical excitation energies and UV-vis spectra. Our results clearly provide a benchmark calibration of the TD-DFT method for phthalocyanine based dyes and pigments used in industry.

Spectral "Fine" Tuning in Fluorescent Proteins: The Case of the GFP-Like Chromophore in the Anionic Protonation State.

Fluorescent proteins (FPs), featuring the same chromophore but different chromophore-protein interactions, display remarkable spectral variations even when the same chromophore protonation state, i.e. the anionic state, is involved. We examine the mechanisms behind this tuning by means of structural analysis, molecular dynamics simulations, and vertical excitation energy calculations using QM/MM Time-Dependent Density Functional Theory (TD-DFT), CASPT2/CASSCF, and SAC-CI. The proteins under investigation include the structurally similar, though spectrally distinct, Dronpa and mTFP0.7, with absorption peaks at 453 and 503 nm, respectively. We extend our analysis to two Green Fluorescent Protein variants, GFP-S65T (absorption peak at 484 nm), for comparison with previous computational studies, and GFP-S65G/V68L/S72A/T203Y, a yellow fluorescent protein (514 nm), in order to include one of the most red-shifted FPs containing a GFP-like chromophore. We compare different choices of the QM system, and we discuss how molecular dynamics simulations affect the calculation of excitation energies, with respect to X-ray structures. We are able to partially reproduce the spectral tuning of the FPs and correlate it to the chromophore bond-length variations, as determined by specific interactions with the chromophore environment.

Benchmarking the performance of time-dependent density functional methods

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small- to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.

Theoretical calculation about the valence and rydberg excited states of hydrogen cyanide

The singlet and triplet excited states of hydrogen cyanide have been computed by using the complete active space self-consistent field and completed active space second order perturbation methods with the atomic natural orbital (ANO-L) basis set. Through calculations of vertical excitation energies, we have probed the transitions from ground state to valence excited states, and further extensions to the Rydberg states are achieved by adding 1s1p1d Rydberg orbitals into the ANO-L basis set. Four singlet and nine triplet excited states have been optimized. The computed adiabatic energies and the vertical transition energies agree well with the available experimental data and the inconsistencies with the available theoretical reports are discussed in detail.

Solvent- and Temperature-Dependent Conformational Changes between Hückel Antiaromatic and Möbius Aromatic Species in meso-Trifluoromethyl Substituted [28]Hexaphyrins

We investigated the photophysical properties of figure-eight-like meso-hexakis(trifluoromethyl) [26]- and [28]hexaphyrins(1.1.1.1.1.1) denoted as TFM26H and TFM28H, respectively, using steady-state and time-resolved spectroscopy along with theoretical calculations to explore their electronic and magnetic natures depending on their molecular aromaticity. TFM26H exhibited a well-resolved absorption feature and intense fluorescence, both of which were neither solvent- nor temperature-dependent. These optical properties were in agreement with its Hückel's [4n + 2] aromaticity as observed in typical aromatic porphyrinoids. The S(1)-state lifetime of ~50 ps for TFM26H in solution was shorter than those in planar aromatic hexaphyrins (>100 ps) presumably due to nonplanar figure-eight geometry of TFM26H. However, TFM28H exhibited remarkable changes in solvent- and temperature-dependent absorption spectra as well as excited-state lifetimes indicating that a dynamic equilibrium occurs between the two conformational species. With the help of quantum mechanical geometry optimization and vertical excitation energy calculations, we found that the figure-eight double-sided conformer observed in the solid-state and single-sided distorted one could be the best candidates for the two conformers, which should be Hückel antiaromatic and Möbius aromatic species, respectively, based on their optical characteristics, molecular orbital structures, and excited-state lifetimes. Conformational dynamics between these two conformers of TFM28H was scrutinized in detail by temperature-dependent (1)H NMR spectra in various solvents, which showed that the conformational equilibrium was quite sensitive to solvents and that a conformational change faster than the NMR time-scale occurs even at 173 K.

Solvent‐Dependent Aromatic versus Antiaromatic Conformational Switching in meso‐(Heptakis)pentafluorophenyl [32]Heptaphyrin

We have investigated conformational switching dynamics of meso-heptakis(pentafluorophenyl) [32]heptaphyrin(1.1.1.1.1.1.1) in various solvents using steady-state, time-resolved, and temperature-dependent spectroscopy. Absorption and fluorescence spectra of [32]heptaphyrin are quite sensitive to solvent environments. In nonpolar toluene, the antiaromatic figure-of-eight conformation is dominant, as seen in the X-ray crystallography, based on broad and weak absorption bands without any fluorescence and moderate paratropic ring current. On the other hand, a well-resolved sharp absorption spectrum, strong fluorescence, and diatropic ring current in the 1H NMR spectrum in slightly polar THF indicate that most of [32]heptaphyrin molecules take significantly distorted Möbius conformation with aromatic character. By using transient absorption (TA) spectroscopy, the lowest singlet excited-state lifetimes have been revealed to decay biexponentially with the time constants of 5 and 65 ps for figure-of-eight and Möbius conformations, respectively. Based on these results along with vertical excitation energy calculations, we are able to assign two conformers as Hückel antiaromatic and Möbius aromatic species, respectively; it shoulf be noted that the aromaticity/antiaromaticity does not change with temperature variation. Interestingly, in moderately polar solvent, ethyl ether, we find out that these two conformational isomers coexist with a dynamic equilibrium, as revealed by excitation-wavelength-dependent TA, temperature-dependent absorption and 1H NMR spectra. Through our findings, we have demonstrated that the conformational switching dynamics between Hckel antiaromatic and Möbius aromatic conformers in [32]heptaphyrin(1.1.1.1.1.1.1) are strongly affected by solvent medium as well as temperature.

Electronic spectrum of F2CO: theoretical calculations of vertical excitation energies and intensities

In this work, the linear response formalism with a triples-corrected CCSD reference wave function, LR-CCSDR(3), is applied to the calculation of vertical excitation energies of singlet states of the F2CO molecule. A basis set of atomic natural orbitals augmented with a series of Rydberg functions has been used in the calculations. A large number of electronically excited states were calculated, and the valence, Rydberg, or mixed character of the states were investigated. In addition, the molecular quantum defect orbital (MQDO) method has been used to determine transition intensities involving Rydberg states. Excitation energies and transition intensities for Rydberg states with n > 3 are reported for the first time.

Theoretical study of the low-lying electronic states of CCCF radical and its ions

The low-lying electronic states of the CCCF radical and its ionic states have been investigated systematically using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods in conjunction with aug-cc-pVTZ basis set. To investigated the Renner–Teller effect on the CCCF radical, Cs symmetry was used for CCCF. The CCCF has been found to have a X2A′ ground state with rotational constant B¯=4500.5MHz, which is in good agreement with the experimental values of 4555.8043MHz. The calculations of vertical excitation energies of CCCF at 2.893 and 4.180eV are attribute to the X2A′→32A″ and X2A′→52A′, respectively, which has larger oscillator strengths. The ionization potentials of CCCF are computed in order to provide a theoretical guidance to the photoelectron spectrum (PES) of the CCCF radical. The first adiabatic electron affinity (AEA) of CCCF is predicted to be 2.671eV. A comparison of the geometries and bonding among the CCCX (X=F, Cl, and Br) radicals presents the ground state X2A′ of CCCX can be described as allenic structures with the unpaired electron on the C3 atom, while the excited state 12A″ (12Π) of CCCX have the linear acetylenic structures with the unpaired electron on the C1 atom. The barriers to linearity decrease as follows: ΔE (CCCF)<ΔE (CCCCl)<ΔE (CCCBr).

Multireference Generalized Van Vleck Perturbation Theory (GVVPT2) Study of the NCO + HCNO Reaction: Insight into Intermediates†

Possible mechanisms for the NCO + HCNO reaction, previously studied using single reference methods, have been revisited using the second-order generalized Van Vleck perturbation theory (GVVPT2) variant of multireference perturbation theory. Large scale GVVPT2 calculations, with 25 active orbitals, demonstrate that the electronic structures of the ground states of all eight previously identified plausible doublet spin intermediates of this reaction are substantially multiconfigurational with maximum configuration amplitudes not larger than 0.87. Moreover, comparison of GVVPT2 results with underlying MCSCF calculations demonstrates a pronounced effect of dynamic correlation on the configurational structure. GVVPT2 calculations of vertical excitation energies of the intermediates showed that all the intermediates, except one, have significant excitation energies to both the same and other spatial symmetries as the ground states. The relative GVVPT2 energies of the intermediates were found to be consistent with earlier calculations, including the prediction of a negative temperature dependence of the rate constant, and support available experimental observations.

Excited and ionized states of the ozone molecule with full triples coupled cluster methods

The role of connected triple excitations in coupled cluster (CC) calculations of vertical excitation energies, ionization potentials, and the electron affinity of the ozone molecule is evaluated. The equation of motion (EOM) and Fock space (FS) multireference CC approaches with full triples have been used in the calculations. The effect of the T(3) and R(3) operators significantly improve the EOM CCSD results for all considered quantities. A similar behavior is observed in the case of the FS-CC calculations. The FS-CC calculations with full triples have been obtained only for the intermediate Hamiltonian realization of the FS approach as the standard formulation diverges. The latter results are rigorously linked, and less expensive since smaller matrices are diagonalized.

Benchmarking Second Order Methods for the Calculation of Vertical Electronic Excitation Energies: Valence and Rydberg States in Polycyclic Aromatic Hydrocarbons

The performance of the six second order linear response methods RPA(D), SOPPA, SOPPA(CCSD), CIS(D), CC2, and CCSD, which include either noniterative or iterative doubles contributions, has been studied in calculations of vertical excitation energies. The benchmark set consisted of 39 valence and 76 Rydberg states of benzene and five polycyclic aromatic hydrocarbons. As reference values we have used the results of the corresponding calculations with the third order method CCSDR(3), which includes noniterative triples contributions. In addition we have also carried out equivalent calculations at the level of the random phase approximation as well as with the configuration interaction singles and multireference configuration interaction singles and doubles methods.

Multiconfigurational time-dependent Hartree-Fock calculation of vertical excitation energies and transition moments of O2

Excitation energies and oscillator strengths in the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approximation are presented for the O2 molecule. Variations of excitation energies with respect to the diffuse character of the basis set are examined. The equivalence between oscillator strengths calculated in the dipole length and dipole velocity approximation in the MCTDHF approximation is investigated.

Rydberg, valence and mixed states in the vertical spectrum of HF

Size-consistent self-consistent multireference singles and doubles configuration interaction (SC) 2–MR–SDCI, and linear response coupled cluster of singles and doubles including triples LR–CCSDR(3) methods, with a basis set of ANO’s augmented with a single series of molecular Rydberg functions, have been applied to the calculation of vertical excitation energies of HF in the 10–16 eV region. Special care has been put in the description of the valence, Rydberg and mixed states. Some advantage has been taken from the different physical contents of the methods to discuss some assignments. The (4,5) f Rydberg states of HF are predicted at 15.2 and 15.5 eV.

Aromatic versus Antiaromatic Effect on Photophysical Properties of Conformationally Locked trans-Vinylene-Bridged Hexaphyrins

We have investigated the electronic structures and energy relaxation dynamics of vinylene-bridged hexaphyrins using steady-state and time-resolved spectroscopies along with theoretical calculations in order to reveal their aromaticity-dependent electronic and magnetic properties. Ethynyl-TIPS-substituted planar and rectangular [28]hexaphyrin, regarded as a Huckel antiaromatic compound, tends to adopt a twisted Mobius aromatic topology via structural distortion in order to reduce the total internal energy, in contrast to aromatic [26]hexaphyrin, which maintains a planar conformation in solution. Spectacles-shaped vinylene-bridged [26]- and [28]hexaphyrins represent highly Huckel aromatic and antiaromatic natures, respectively, as revealed by NMR spectroscopy, giving rise to remarkable differences in NICS(0) and HOMA values and shapes of steady-state absorption and emission spectra. In particular, lifetime of the lowest singlet excited state of [28]hexaphyrin (8.6 ps) is 30 times shorter than that of the aromatic congener [26]hexaphyrin (282 ps), as measured by the femtosecond transient absorption technique. Both frontier molecular orbital analyses and vertical excitation energy calculations suggest that vinylene-bridged [28]hexaphyrin has an optically dark lowest singlet state in the NIR region, as observed in the absorption spectrum with a very low oscillator strength, which might act as a ladder state in the excited-state energy relaxation dynamics. Our findings provide further insight into the aromaticity-driven electronic properties of various porphyrinoids as well as of aromatic/antiaromatic hydrocarbon systems.

Benchmarks for Electronically Excited States: A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods: CCSDR(3) versus CC3.

CCSDR(3) calculations of vertical excitation energies are reported for a set of 24 molecules and 121 excited valence singlet states from a recently published benchmark of organic molecules. The same geometries (MP2/6-31G*) and basis set (TZVP) were employed as in our previous linear response CC2, CCSD, and CC3 calculations. The CCSDR(3) results are compared against the CCSD and CC3 results. Statistical evaluation of all CCSDR(3) excitation energies gives mean absolute deviations of 0.09 eV from CC3 and 0.30 eV from CCSD. For excited states, which are dominated by single excitations, the absolute mean deviation from CC3 is reduced to 0.02 eV and the maximum deviation is 0.09 eV. CCSDR(3) is thus a very cost-effective accurate alternative to CC3.

Large-scale parallel calculations with combined coupled cluster and molecular mechanics formalism: Excitation energies of zinc–porphyrin in aqueous solution

The need for combined QM/MM approaches with high-level coupled cluster (CC) methods in the QM core is unquestionable. In an effort to make these methods widely applicable, the scalability of CC approaches across hundreds/thousands of CPUs will play a central role. In this Letter we report the performance of our CC codes in calculations of vertical excitation energies of low-lying excited states of the zinc–porphyrin molecule in aqueous solution. Coupled cluster description of excited states is based on equation-of-motion approach with singles and doubles (EOMCCSD) as well as its non-iterative extension for triply excited configurations. These results are compared with those obtained with time-dependent density functional theory (TD-DFT).