Jörg Tatchen

Spin‐orbit coupling of DFT/MRCI wavefunctions: Method, test calculations, and application to thiophene

During the past decade the one‐center mean‐field approximation has proven to be a very appropriate framework for the accurate description of spin‐orbit effects at the correlated all‐electron level. Here, a new efficient code, SPOCK, is introduced that calculates spin‐orbit matrix elements in the one‐center mean‐field approximation for multireference CI wave functions. For the first time, the computation of spin‐dependent interactions within a Kohn‐Sham orbital based CI (DFT/MRCI) scheme 1 is made possible. The latter approach is suitable for large scale systems with up to 100–200 valence electrons. Test calculations are performed on well‐known diatomic molecules and the thiocarbonyl pyranthione. Spin‐orbit matrix elements show good agreement with their Hartree‐Fock orbital based counterparts but are obtained at considerably lower expense, thus demonstrating the power of the method. As an application singlet‐triplet couplings in thiophene are investigated that are important for the photophysics and photochemistry. Spin‐orbit matrix elements between all π → π* excited states are found to be small. Considerably larger spin‐orbit matrix elements are observed only for cases in which π → σ* excited configurations are involved.

Singlet and Triplet Excited States and Intersystem Crossing in Free‐Base Porphyrin: TDDFT and DFT/MRCI Study

Extensive time-dependent DFT (TDDFT) and DFT/multireference configuration interaction (MRCI) calculations are performed on the singlet and triplet excited states of free-base porphyrin, with emphasis on intersystem crossing processes. The equilibrium geometries, as well as the vertical and adiabatic excitation energies of the lowest singlet and triplet excited states are determined. Single and double proton-transfer reactions in the first excited singlet state are explored. Harmonic vibrational frequencies are calculated at the equilibrium geometries of the ground state and of the lowest singlet and triplet excited states. Furthermore, spin-orbit coupling matrix elements of the lowest singlet and triplet states and their numerical derivatives with respect to nuclear displacements are computed. It is shown that opening of an unprotonated pyrrole ring as well as excited-state single and double proton transfer inside the porphyrin cavity lead to crossings of the potential energy curves of the lowest singlet and triplet excited states. It is also found that displacements along out-of-plane normal modes of the first excited singlet state cause a significant increase of the , , and spin-orbit coupling matrix elements. These phenomena lead to efficient radiationless deactivation of the lowest excited states of free-base porphyrin via intercombination conversion. In particular, the S1-->T1 population transfer is found to proceed at a rate of approximately 10(7) s(-1) in the isolated molecule.

SPOCK.CI: A multireference spin-orbit configuration interaction method for large molecules

We present SPOCK.CI, a selecting direct multireference spin-orbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spin-free density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] and includes spin-orbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective one-electron spin-orbit atomic mean-field Hamiltonian, the application of a resolution-of-the-identity approximation to computationally expensive spin-free four-index integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spin-dependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Second-order properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sum-over-state approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on 4H-pyran-4-thione, dithiosuccinimide, and free-base porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of free-base porphin, MRSOCI calculations can easily be run on a single-processor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.

Time-dependent approaches for the calculation of intersystem crossing rates

We present three formulas for calculating intersystem crossing rates in the Condon approximation to the golden rule by means of a time-dependent approach: an expression using the full time correlation function which is exact for harmonic oscillators, a second-order cumulant expansion, and a short-time approximation of this expression. While the exact expression and the cumulant expansion require numerical integration of the time correlation function, the integration of the short-time expansion can be performed analytically. To ensure convergence in the presence of large oscillations of the correlation function, we use a Gaussian damping function. The strengths and weaknesses of these approaches as well as the dependence of the results on the choice of the technical parameters of the time integration are assessed on four test examples, i.e., the nonradiative S(1) ⇝ T(1) transitions in thymine, phenalenone, flavone, and porphyrin. The obtained rate constants are compared with previous results of a time-independent approach. Very good agreement between the literature values and the integrals over the full time correlation functions are observed. Furthermore, the comparison suggests that the cumulant expansion approximates the exact expression very well while allowing the interval of the time integration to be significantly shorter. In cases with sufficiently high vibrational density of states also the short-time approximation yields rates in good agreement with the results of the exact formula. A great advantage of the time-dependent approach over the time-independent approach is its excellent computational efficiency making it the method of choice in cases of large energy gaps, large numbers of normal modes, and high densities of final vibrational states.

Ab initio spectroscopy and photoinduced cooling of the trans-stilbene molecule

We present a theoretical study of the S(0)-->S(1) and S(0)<--S(1) vibronic spectra for trans-stilbene. Franck-Condon spectra in the harmonic approximation are generated for the complete system with 72 degrees of freedom by means of an analytic time-dependent approach accounting for Dushinsky rotations and thermal effects. The force fields are computed by means of density functional theory (DFT) and time-dependent DFT, on the one hand, and ab initio complete active space self-consistent field theory, on the other hand. The B3LYP functional shows that almost planar potential energy surface minima are found for the S(0) and S(1) state. Imposing C(2h) symmetry constraints, we obtain low-temperature high-resolution Franck-Condon spectra for both absorption and emission which are in reasonably good agreement with the experimental spectra measured by Syage et al. [J. Chem. Phys. 81, 4685 (1984)] in supersonic jets. Due to thermal population of low-energy modes, the room temperature absorption spectrum is very broad. An almost structureless band which extends over several thousand cm(-1) is obtained from the present theory and agrees with the experimental absorption band shape. Finally, within the harmonic model, we study the effect of photoexcitation on the energy distribution in the excited S(1) state. We find noticeable cooling of approximately 20 K within a frequency interval spanning from -400 to 200 cm(-1) around the 0-0 transition. This indicates that photoinduced cooling must be taken into account when considering the dynamics of the photoinduced isomerization of trans-stilbene. Moreover, this is not the final word, as anharmonicity of the low frequency modes must be taken into account to obtain a full picture which would explain both the energy dependence of the isomerization rates as well as the dependence on the pressure of an external buffer gas.

Intersystem crossing driven by vibronic spin-orbit coupling : a case study on psoralen

For 7H-furo[3,2-g][1]benzopyran-7-one (psoralen), intersystem crossing (ISC) rate constants have been computed. Employing the Fermi golden rule, the harmonic approximation, and a pure-spin Born-Oppenheimer basis, both direct and vibronic spin-orbit (SO) coupling has been taken into account. Necessary data on electronic excitation energies and potential energy hypersurfaces originate from correlated all-electron calculations applying (time-dependent) density functional theory and the density functional theory/multireference configuration interaction approach. SO coupling has been treated by means of the one-center mean-field approximation. Vibronic SO couplings have been evaluated via numerical differentiation of SO matrix elements. Accounting only for direct SO coupling, rate constants of the order of k(ISC) approximately 10(10) s(-1) result for S2(n --> pi*) --> T1(pi --> pi*) ISC, whereas the rates of the channels S1 (pi --> pi*) --> {1,2 3} (pi --> pi*) do not exceed k(ISC) approximately 10(5) s(-1). Including vibronic SO coupling, rate constants of k(ISC) approximately 3 x 10(8) s(-1) are obtained for the S1 (pi --> pi*) --> T1 (pi --> pi*) ISC. The radiationless transition from the S1(pi --> pi*) state to the nearly degenerate T3(pi --> pi*) state has been estimated to be slightly less efficient (k(ISC) approximately 10(7) s(-1)). Based on our computed rates of ISC and excited state solvent shifts, we conclude that the experimentally observed appreciable triplet quantum yields of psoralen in polar protic media are primarily due to S1(pi --> pi*) --> T (pi --> pi*) channels. For heteroaromatic systems, (pi --> pi*)/(pi --> pi*) ISC driven by vibronic SO coupling is expected to be a common triplet state population mechanism.

Semiclassical on-the-fly computation of the S0→S1 absorption spectrum of formaldehyde

The anharmonic S(0)-->S(1) vibronic absorption spectrum of the formaldehyde molecule is computed on the fly using semiclassical dynamics. This first example of an on-the-fly semiclassical computation of a vibronic spectrum was achieved using a unit prefactor modified frozen Gaussian semiclassical propagator for the excited state. A sample of 6000 trajectories sufficed for obtaining a converged spectrum, which is in reasonable agreement with experiment. Similar agreement is not obtained when using a harmonic approximation for the spectrum, demonstrating the need for a full anharmonic computation. This first example provides a resolution of approximately 100 cm(-1). Potential ways of improving the methodology and obtaining higher resolution and accuracy are discussed.

ON THE PERFORMANCE OF APPROXIMATE SPIN-ORBIT HAMILTONIANS IN LIGHT CONJUGATED MOLECULES : THE FINE-STRUCTURE SPLITTING OF HC6H+, NC5H+, AND NC4N+

Abstract Spin–orbit calculations have been performed on the carbon-rich radical cations HC6H+, NC5H+, and NC4N+ using the full one-and two-electron no-pair spin–orbit Hamiltonian and more approximate approaches. It is found that the full operator can be replaced by an effective one-electron mean-field spin–orbit Hamiltonian almost without loss of accuracy. An analysis of the approximations reveals that multi-center integrals are large, but one- and two-electron terms tend to cancel. The one-center spin–orbit mean-field approach yields fine-structure splittings within 5% of the full results and thus appears to be a favorable means to reliably predict rates of spin-forbidden processes in organic molecules at low cost.

Tautomers and electronic states of jet-cooled 2-aminopurine investigated by double resonance spectroscopy and theory

We present resonant two-photon ionization (R2PI), IR-UV, and UV-UV double resonance spectra of jet-cooled 2-aminopurine (2AP) as well as Fourier transform infrared (FTIR) gas phase spectra. 2AP is a fluorescing isomer of the nucleobase adenine. The results show that there is only one tautomer of 2AP which absorbs in the wavelength range 32,300-34,500 cm(-1). The comparison with the calculated IR spectra of 9H- and 7H-2AP points to 9H-2AP as the dominating tautomer in the gas phase but the spectra are too similar to allow an unambiguous assignment to the respective tautomer. Hence, we determined vertical and adiabatic excitation energies of both tautomers employing combined density functional theory and multi-reference configuration interaction techniques. For the 0-0 band of the first 1pipi* transition of 9H-2AP we obtain a theoretical value of 32,328 cm(-1), in excellent agreement with the band origin of our R2PI spectrum at 32,371 cm(-1). The first singlet pipi* transition of the less stable 7H-2AP tautomer is predicted to be red-shifted by about 1700 cm(-1) with respect to the corresponding transition in 9H-2AP. From the absence of experimental bands in the energy region between 30,300 and 32,350 cm(-1) we conclude that 7H-2AP is not present to an appreciable extent in the molecular beam. Our calculations yield nearly equal energies for the 1npi* and 1pipi* minima of isolated 2AP, similar to the situation in adenine. The hitherto existing argument that the energetic order of states is responsible for the different spectroscopic properties of these isomers therefore does not hold. Rather, vibronic levels close to the origin of the 1pipi* transition cannot access the conical intersection between the 1pipi* and S(0) states along a puckering coordinate of the six-membered ring, in contrast to the situation in electronically excited 9H-adenine. As a consequence, a rich vibrational structure can be observed in the R2PI spectrum of 2AP whereas the spectrum of 9H-adenine breaks off at low energies.

Vibronic absorption, fluorescence, and phosphorescence spectra of psoralen: a quantum chemical investigation

Excited state potential energy hypersurfaces of 7H-furo[3,2-g][1]benzopyran-7-one (psoralen) have been explored employing (time-dependent) Kohn-Sham density functional theory. At selected points, we have determined electronic excitation energies and electric dipole (transition) moments utilizing a combined density functional/multireference configuration interaction method. Spin-orbit coupling has been taken into account employing an efficient, non-empirical spin-orbit mean-field Hamiltonian. Franck-Condon factors have been computed for vibrational modes with large displacements in the respective Dushinsky transformations. The simulated band spectra closely resemble experimental band shapes and thus validate the theoretically determined nuclear structures at the S(0), S(1), and T(1) minima. In the S(1) (pi(HOMO)-->pi*(LUMO)) state, the lactone bond of the pyrone ring is significantly elongated. From excited vibrational levels of the S(1) state a conical intersection between a (pi-->sigma*) excited state and the electronic ground state may be energetically accessible. Fast non-radiative decay via this relaxation pathway could explain the low fluorescence quantum yield of psoralen. The T(1) (pi(HOMO-1)-->pi*(LUMO)) exhibits a diradicaloid electronic structure with a broken C(5)-C(6) double bond in the pyrone ring. A variational multireference spin-orbit configuration interaction procedure yields a phosphorescence lifetime of 3 s, in excellent agreement with experimental estimates.