1B2u State Research Articles

Laser spectroscopy of free pentacene molecules (II): Stark effect of the vibrationless S1←S transition

Laser Stark spectroscopy has been performed for the first time on free pentacene molecules seeded in a highly collimated supersonic argon beam. The Stark effect of the vibrationless S1←S0 transition of pentacene at 18 649 cm−1 was investigated in a static homogeneous electric field up to 81 kV/cm. Within the unresolved rotational structure, an unexpected large quadratic Stark effect was observed. An analysis of the shifts of sub-band heads and characteristic structures was performed by simulating the complete Stark spectrum using second-order perturbation theory. Surprisingly large values for the differences of the molecular polarizability between the electronic ground state X 1A1g and the excited A 1B2u state were found: ΔP̄=1/3(ΔPaa+ΔPbb+ΔPcc)=9.1(3)×102 Å3, ΔPcc=Pcc′−Pcc″=13.7(8)×102 Å3, ΔPxx=−1.4(8)×102 Å3, ΔPyy=15.0(7)×102 Å3 (x=a, y=b, or vice versa). Attributing the in-plane axes uniquely and the determination of the ground state anisotropy was not possible. It is assumed that the large polarizability of the excited state is dominated by contributions of low-frequency vibrational levels. Indications for deviation from second-order perturbation theory are observed.

A revised MRCI-algorithm coupled to an effective valence-shell Hamiltonian. II. Application to the valence excitations of butadiene

In Paper I of this work we have sketched an improved MRCI algorithm and its coupling to the effective valence-shell Hamiltonian OM2. To check the quality of the resulting OM2/MRCI approach, it is applied here to the excited valence states of all-trans butadiene. As is explained by a review of previous theoretical work, proper descriptions of these states posed severe problems within correlated ab initio treatments but seemed to be trivial within simple correlated π-electron models. We now show that an extended MRCI treatment of the correlations among all valence electrons as described by OM2 closely reproduces the experimental evidence, placing the vertical 2 1Ag excitation by about 0.2 eV below the 1 1Bu excitation. By an analysis of σ–π interactions we explain the corresponding earlier success of correlated π-electron theory. Exploiting the enhanced capabilities of the new approach we investigate the potential surfaces. Here, OM2/MRCI is shown to predict that the 2 1Ag state is energetically lowered about four times more strongly than the 1 1Bu state upon geometry relaxation constrained to the C2h symmetry. We conclude that OM2/MRCI should be well-suited for the study of excited state surfaces of organic dye molecules.

Theoretical Study of the Lowest1BUStates oftrans-Stilbene

The results of a theoretical study of the ground state, 11Ag, and of the lowest 1Bu states of trans-stilbene are presented. The vertical and adiabatic excitation energies of the lowest 1Bu states have been computed using multiconfigurational SCF theory, followed by second-order perturbation theory. It is shown that the two lowest excited states are separated by a small energy gap in the Franck−Condon region. They are the 11Bu, characterized by the HOMO→LUMO single excitation substantially localized on the ethylenic moiety, and the 21Bu, formed by a combination of one electron excitations localized mainly on the benzene rings. The most intense transition is found to be the lowest in energy when the interaction between different states is included at the level of second-order perturbation theory. The vibronic structure of emission and absorption spectra of the two lowest 1Bu states have been determined within the Franck−Condon approximation. The spectrum calculated for the 11Bu state agrees with the experimental spectrum, while the low intensity band computed for the 21Bu state has no experimental counterpart. It is concluded that this band is buried in the strong 11Bu absorption and therefore not observed.

The Doppler-free two-photon absorption spectroscopy of naphthalene with Zeeman effects

The Doppler-free spectrum and the Zeeman effect of the A 1B1u(v4=1:b1u)←X 1Ag(v=0) transition of naphthalene in the 33 576.4–33 578.0 cm−1 range has been measured by means of two-photon absorption spectroscopy with counter propagating light beams of identical wavelength within an external cavity. Rotational lines were fully resolved, and 1098 Q(K)Q(J) lines of J=0–42, K=0–24 were assigned. The molecular constants of the A 1B1u(v4=1:b1u) state were determined. Deviations from the line positions calculated using the molecular constants were observed for several lines. Perturbations were not observed for K=0 but were observed to increase with increasing K. The perturbations were therefore identified as originating from a parallel Coriolis interaction. The Zeeman splittings for lines of a given J were observed to be maximum at K=0 and to decrease with increasing K. Analysis of these results indicate that the magnetic moment lies along the c axis (perpendicular to the molecular plane). Any lines broader than our instrumental resolution (5 MHz) were not observed at H=0 T. The J and K dependence of the Zeeman splittings of the A 1B1u(v4=1:b1u)←X 1Ag(v=0) transitions were observed to be regular. This observation and the small number of perturbed lines, leads to the conclusion that the resonance interaction of the A 1B1u state with the T1 3B3u and T2 3B1u states are small and negligible in the observed region.

Excited State Properties of C6H6 and C6D6 Studied by Feynman Path Integral−ab Initio Simulations

The Feynman path integral Monte Carlo formalism has been combined with an ab initio configuration interaction approach in order to analyze the excited singlet states of the benzene isomers C6H6 and C6D6 under the conditions of thermal equilibrium. Electronic transition energies PIĒT and oscillator strength PIfosc, which have been sampled over large sets of nuclear configurations, are compared with single-configuration results ET, fosc. The latter set of quantities has been derived for the D6h energy minimum of benzene. The present quantum Monte Carlo simulations lead to a simple physical picture for the nonzero intensities of the transitions to the two lowest excited singlet states of the two benzene isomers. Under D6h conditions, the transitions to the 1B2u and 1B1u states are dipole-forbidden. The influence of the nuclear degrees of freedom on the excited-state properties of the two π rings up to room temperature is quantum driven. The quantum fluctuations of the nuclei on a potential energy surface wi...

S 1 /S 2 exciton splitting in the (2-pyridone)2 dimer

The S1↔S0 and S2↔S0 vibronic spectra of the supersonically cooled 2-pyridone dimer (2PY)2 and its 13C-, d1-, and d2-isotopomers were investigated by two-color resonant two-photon ionization and fluorescence spectroscopies. For the C2h symmetric (2PY)2–h2 and (2PY)2–d2 complexes, the 2PY moieties are equivalent and the S1↔S0 (1Ag↔1Ag) transition is forbidden. A single H/D or 12C/13C isotopic substitution reduces the symmetry to Cs, so that (2PY)2–13C and (2PY)2–d1 both exhibit S1↔S0 and S2↔S0 transitions. The S1/S2 state exciton splittings are 43.6 cm−1 and 52.4 cm−1, respectively. These are analyzed in terms of a Frenkel model and compared to calculated splittings based on ab initio monomer transition dipole moments. For (2PY)2–d1, whose 2PY subunits are different, an excitation transfer time of 318 fs is calculated from the exciton splitting. The S1↔S0 and S2↔S0 spectra are analyzed and assigned. Several bu intermolecular vibrations of S1 appear via vibronic coupling to the S2(Bu) state. Combination of the fluorescence data from excitation of the S1 and S2 origins and vibrational excitations of (2PY)2–h2, (2PY)2–d1, and (2PY)2–d2 allows the determination of the six S0 state intermolecular vibrational frequencies.

Doppler-free two-photon absorption spectroscopy and the Zeeman effect of the A 1B2u←X 1A1g14111 band of benzene

A Doppler-free absorption spectrum and the Zeeman effect of the A 1B2u(v14=1,v1=1)←X 1A1g(v=0) transition of benzene have been measured by means of two-photon absorption spectroscopy with counterpropagating light beams of identical wavelength within an external cavity. Rotational lines were fully resolved, and 647 QQ lines of J=0–43, K=0–43 have been assigned. The molecular constants of the A 1B2u(v14=1,v1=1) state have been determined as A=B=0.181 046 1, C=0.090 548 9, DJ=0.544×10−7, DJK=−1.093×10−7, DK=0.587×10−7, and T0=40 578.2672 cm−1. The Zeeman splittings for lines of a given J were observed to increase regularly with K and reach a maximum at K=J. This demonstrates that the magnetic moment lies along the c axis (perpendicular to the molecular plane). The magnetic moment of the A 1B2u(v14=1,v1=1,J=43,K=43) level was determined to be 0.005μB. The Zeeman splittings of the K=J levels were observed to increase with increasing J. Via analysis of the rotationally resolved Zeeman spectra, it is concluded that the A 1B2u state is mixed with the E2u3 state. This new finding suggests that vibronic interactions between E2u3 and B1u3(T1) and between E2u3 and E1u3(T2) through the mixed E2u3 component, contribute to the B2u1(S1)→3B1u(T1) and B2u1(S1)→3E1u(T2) intersystem crossings, respectively.

Excited state polarizabilities of conjugated molecules calculated using time dependent density functional theory

In this paper, time-dependent density functional theory (TDDFT) calculations of excited state polarizabilities of conjugated molecules are presented. The increase in polarizability upon excitation was obtained by evaluating the dependence of the excitation energy on an applied static electric field. The excitation energy was found to vary quadratically with the field strength. The excess polarizabilities obtained for singlet excited states are in reasonable agreement with the experimental results for the shorter oligomers, particularly if the experimental uncertainties are considered. For longer oligomers the excess polarizability is considerably overestimated, similar to DFT calculations of ground state polarizabilities. Excess polarizabilities of triplet states were found to be smaller than those for the corresponding singlet state, which agrees with experimental results that are available for triplet polarizabilities. Negative polarizabilities are obtained for the lowest singlet Ag states of longer oligomers. The polarizability of the lowest Bu and Ag excited states of the conjugated molecules studied here are determined mainly by the interaction between these two states. Upon application of a static electric field a quadratic Stark effect is observed in which the lower Bu state has a positive excess polarizability and the upper Ag state exhibits a decrease in polarizability upon excitation. All results are explained in terms of a sum-over-states description for the polarizability.

Vibronic couplings and radiationless transitions between the lowest 1Bu and the first excited 2Ag state of linear polyenes

Transoctatetraene is studied as a model compound by means of ab initio (GAMESS) calculations to study the vibronic coupling between the lowest excited Ag state and the dipolar allowed second excited Bu state. It is found that the evaluated couplings to totally symmetric modes in combination to those of Bu-symmetry can describe the high resolution absorption excitation and emission spectra in more detail. The strong vibronic couplings can further explain the fast internal conversion between the 1Bu and the 2Ag state. It is argued that they can also induce a resonance energy transfer which can compete with a quadrupolar coupling at room temperature. The vibronic transfer mechanism is also discussed for photosynthetic systems including the transfer from carotenoids to bacteriochlorophylls.

Excited-State Dynamics of all-trans-1,3,5,7-Octatetraene in Solution. Direct Observation of Internal Conversion from the S2 to S1 State and Relaxation Processes in the S1 State

Femtosecond transient absorption spectroscopy was used to study the excited-state dynamics of the S2 (11Bu) state all-trans-1,3,5,7-octatetraene in solution. The sample was excited at 267 nm and probed at eleven different wavelengths from 340 to 540 nm. Combined with the picosecond fluorescence spectroscopy, this study allows direct observation of the initial excited-state dynamics of all-trans-1,3,5,7-octatetraene and the subsequent relaxation process to the ground state. Transient absorption signals decaying on time scales of about 0.4 ps were seen at wavelengths longer than 480 nm. These absorptions are assigned to an Sn-S2 transition, indicating that internal conversion from the S2 to S1 state takes place on a 400-fs time scale. The transient absorption signals observed at shorter wavelengths, which correspond to the Sn-S1 transition, decay on a picosecond to subnanosecond time scale. A weak fluorescence at about 300−350 nm, originating from the S2 state, and a strong fluorescence at about 350−500 nm,...

Ultrafast dynamics of the 11Bu-state of 1,3-butadiene after excitation at 204 nm

The ultrafast dynamics of the 11Bu state of 1,3-butadiene was investigated in real time in a femtosecond pump–probe experiment utilizing the RE2PI scheme. A lifetime of 35 ± 10 fs was found for the 11Bu state of the jet-cooled molecule.

Excitation Energies from Time-Dependent Density Functional Theory for Linear Polyene Oligomers: Butadiene to Decapentaene

Time-dependent density functional theory (TDDFT) is applied to calculate vertical excitation energies of trans-1,3-butadiene, trans−trans-1,3,5-hexatriene, all-trans-1,3,5,7-octatetraene, and all-trans-1,3,5,7,9-decapentaene. Attachment and detachment densities for transitions in butadiene and decapentaene from the ground state to the 2 1Ag and 1 1Bu excited states are also calculated and analyzed. Based on comparisons with experimental results and high level ab initio calculations in the literature, significant improvement over configuration−interaction singles is observed for the 2 1Ag state of the polyenes, which has been known to have significant double excitation character. For the 1 1Bu state, TDDFT underestimates the excitation energy by 0.4−0.7 eV. In this case we have observed a significant difference between the results for TDDFT and TDDFT within the Tamm−Dancoff approximation, both in excitation energies and, at least for butadiene, in the character of the excited state.

Excited electronic states of the anion of 7,7,8,8-tetracyanoquinodimethane (TCNQ)

The doublet and quartet anionic states of TCNQ have been studied at the configuration interaction (CI/PM3) level. Our results support an experimental claim from the Brauman group that not only the ground anionic state but also some excited states of TCNQ− are electronically stable. The core excited 12B3u state is separated from the ground 2B2g anionic state by only 1.2eV at the CI/PM3 level. Two externally excited 2Au and 22B3u anionic states are separated by ca. 2.3eV from the ground 2B2g state and are close in energy to the ground electronic state of the neutral TCNQ. In addition, two quartet anionic states 4B2g and 4B1g are found to be electronically stable with respect to the lowest triplet 3B1u state of the neutral. All these anionic states have minima at D2h geometries. Our results suggest that the 12B3u←2B2g and 22B3u←2B2g transitions contribute to the electronic absorption and electron photodetachment spectra of TCNQ−. This conclusion is based on calculated values of electronic transition energies, oscillator strengths, and excess electron binding energies.

Structure−Property Relationships for Two-Photon Absorbing Chromophores: Bis-Donor Diphenylpolyene and Bis(styryl)benzene Derivatives

The two-photon absorption properties of a series of bis dialkylamino- or diarylamino-substituted diphenylpolyenes and bis(styryl)benzenes have been investigated. Two-photon absorption cross sections, δ, as large as 1420 × 10-50 cm4 s/photon-molecule have been observed for molecules with this general bis-donor structure. The effect of the type and length of the conjugated chain and of dialkylamino or diarylamino substitution on the position and magnitude of the peak two-photon absorptivity is reported. The transition dipole moments for the transitions between the ground state and the first excited singlet state (Mge) and between the first and second excited singlet states (Mee‘) have been estimated using experimental data from the one- and two-photon spectra. It was found that increases in chain length result mainly in an increase in Mge, whereas the addition of donor end groups or going from diphenylpolyene- to phenylene-vinylene-type bridges leads primarily to an increase in Mee‘. The trends in the energy of the lowest excited singlet states and in the transition moments for the diphenylpolyene series as a function of chain length are in agreement with those calculated by quantum mechanical methods. These results furnish a link between structural features in these classes of molecules and the electronic dipole couplings and state energies that control the strength of the two-photon absorption. In bis(aminophenyl)polyenes containing up to four double bonds (m) the lowest excited singlet state is a Bu state, as opposed to the case of simple polyenes and diphenylpolyenes, for which it is an Ag state for m > 2. The relationship of the state ordering in these systems with the observed values of the radiative and nonradiative decay rates is also discussed.

Electronic Excitation in a Saturated Chain: An MS-CASPT2 Treatment of the Anti Conformer of n-Tetrasilane

The singlet−singlet electronic spectrum of the anti conformer of n-tetrasilane has been studied using multiconfigurational wave functions (CASSCF), second-order perturbation theory (CASPT2), and its multi-state extension (MS-CASPT2), in conjunction with large ANO-type basis sets including Rydberg functions. The calculations include the 4s, 4p, and 3d members of the Rydberg series converging on the first ionization. Mixing of valence and Rydberg states observed in the CASSCF wave functions is not fully rectified by single-reference CASPT2 theory, whereas the MS-CASPT2 method separates the valence and Rydberg states effectively. At the MS-CASPT2 level, six valence excited states have been found below the lowest Rydberg transition, predicted at 7.40 eV. In terms of natural orbitals, they correspond to single electron promotions from the σ-symmetry HOMO to four σ* and two π* valence orbitals. Vertical dipole-allowed valence transition energies (oscillator strengths) are computed at 6.33 eV (1.12), 6.68 eV (0.01), and 6.96 eV (0.15), for excitation to 11Bu, 11Au, and 21Bu states, respectively. Three vertical dipole-forbidden valence transitions are predicted to be interleaved among them at 6.55 eV (21Ag), 6.87 eV (31Ag), and 7.10 eV (11Bg). The results are consistent with the available experimental data and are easily rationalized in terms of a simple Hückel model of σ delocalization.

A theoretical study of the 1B2u and 1B1u vibronic bands in benzene

The two lowest bands, 1B2u and 1B1u, of the electronic spectrum of the benzene molecule have been studied theoretically using a new method to compute vibronic excitation energies and intensities. The complete active space (CAS) self-contained field (SCF) method (with six active π-orbitals) was used to compute harmonic force field for the ground state and the 1B2u and 1B1u electronic states. A linear approximation has been used for the transition dipole as a function of the nuclear displacement coordinates. Derivatives of the transition dipole were computed using a variant of the CASSCF state interaction method. Multiconfigurational second-order perturbation theory (CASPT2) was used to obtain absolute excitation energies (12 active π-orbitals). The results show that the approach works well. Vibrational progressions are well described in both bands and intensities, and energies are in agreement with experiment, in particular when CASPT2 derived geometries are used. One interesting result is that computed vertical energies fall about 0.1 eV on the high energy side of the band maximum.

S 1 –S 2 vibronic coupling in trans-1,3,5-hexatriene. II. Theoretical investigation of absorption and resonance Raman spectra

No direct absorption or emission signals of the 2 1Ag state of trans-1,3,5-hexatriene (THT) have been detected so far. However, the ab initio calculations of the three valence singlet states of THT presented in the preceding paper (paper I) put the vertical excitation energy of the 2 1Ag state ca. 0.5 eV below that of the 1 1Bu state. This result indicates possible strong vibronic coupling effects on the spectroscopy of the bright 1 1Bu state. We construct a quantum-mechanical three-state eight-mode model Hamiltonian operator for the microscopic description of the ultrafast S2→S1 internal conversion dynamics following optical excitation of the 1 1Bu state based on the ab initio potential energy information for the S0, S1, and S2 states of THT compiled in paper I. This dynamical model is shown to yield a reliable description of the absorption, preresonance and resonance Raman (RR) spectroscopy of the 1 1Bu state of THT. The homogeneous linewidth of 155 cm−1 FWHM observed for the origin band of the 1 1Ag→11Bu transition can be reproduced with an optical dephasing time T2 of 90 fs. The strong enhancement of 1 1Bu RR bands involving the almost Franck–Condon inactive tuning mode ν9 as well as the observed rapid 1 1Bu population decay indicate that the S1 and S2 states are probably nearly degenerate, the 2 1Ag energy may also be slightly higher than that of the 1 1Bu state vertically. However, the parameter set that yields a realistic description of the RR spectroscopy and population dynamics within the eight-mode vibronic coupling model needs to be modified in order to reproduce the high-resolution 1 1Bu absorption profile, i.e., a significant reduction of the ab initio interstate coupling constants is required. A convergence of the two different parameter sets can be expected if the Hamiltonian is extended by the 28 weakly coupled modes that are considered by a phenomenological relaxation term in the present model.

S 1 –S 2 vibronic coupling in trans-1,3,5-hexatriene. I. Electronic structure calculations

The potential-energy surfaces of the 1 1Ag, 2 1Ag, and 1 1Bu states of trans-1,3,5-hexatriene (THT) are explored in the vicinity of the ground state equilibrium structure. The S0 geometry optimization and force field calculation have been carried out with the restricted Hartree–Fock plus Mo/ller–Plesset second-order perturbation theory method. Vibronic coupling constants for the normal coordinates of ag and bu symmetry were computed with the complete-active-space self-consistent-field (CASSCF) and single state multiconfigurational second-order perturbation theory (CASPT2) electronic structure models. The CASSCF/CASPT2 method unequivocally places the vertical excitation energy of the dark 2 1Ag “phantom state” below the 1 1Bu level and predicts an energy difference of ca. 0.5 eV. The results are consistent with time-resolved photoionization yield and photoelectron spectroscopy experiments that indicate the existence of a low lying S1–S2 conical intersection which induces rapid 1 1Bu→2 1Ag internal conversion on a time scale of 40 fs to 50 fs [Cyr and Hayden, J. Chem. Phys. 104, 771 (1996)]. Based on the vibronic coupling constants five totally symmetric vibrations with high Franck–Condon and/or tuning activity have been identified. The S1 and S2 states interact primarily via the two bu normal modes ν24 and ν26. Other ag and bu normal vibrations do not appear to couple significantly to the lowest lying π→π* transition. The modeling of the ultrafast relaxation processes following optical excitation of the 1 1Bu state of THT and the calculation of absorption and resonance Raman spectra are discussed in the following paper.

On the Vertical and Adiabatic Excitation Energies of the 2Ag State of trans-1,3-Butadiene

The excitation energy to the 21Ag state of trans-1,3-butadiene is examined using a variety of ab initio electronic structure techniques. While analogous states have been shown to be the lowest singlet excited states for all longer polyenes, for butadiene the position of the 21Ag state relative to the HOMO → LUMO excitation (11Bu) has been difficult to establish theoretically. We employ a variety of methods (CASSCF, CASPT2, MRSDCI, QDVPT) to examine both the vertical and adiabatic excitation energies for this state. At the ground-state geometry, the vertical excitation energies obtained by CASPT2 and Davidson-corrected MRSDCI for the 21Ag state differ by approximately 0.15 eV, but all of the methods predict that the 21Ag state has a lower 0−0 excitation energy than the 11Bu state. Possible reasons for the discrepancies between the various methods for the vertical excitation energy are discussed.

On the nature of electronic excitations in poly(paraphenylenevinylene): A quantum-chemical investigation

Correlated quantum-chemical calculations are performed on phenylenevinylene oligomers containing up to eleven repeat units, to characterize the nature of the electronic excitations relevant for the photophysical properties of the corresponding polymer. The focus is first on the nonlinear optical response of model conjugated chains and the simulation of their frequency-dependent (third-harmonic generation, electroabsorption, and two-photon absorption) response. From the assignment of the calculated resonance features, the excited states dominating the third-order nonlinear polarizability are identified and their chain-length dependence is investigated. On that basis, we build an essential-state single-chain model (that includes the 1Bu, 2Ag, mAg, and nBu states) and apply it to the interpretation of recent experimental data reported for poly(paraphenylenevinylene) and derivatives. We then examine how the exciton binding energy, here defined as the difference between the energies of the charge-separated nBu and the strongly optically allowed 1Bu excited states, is affected by both intrachain and interchain polarization effects.