We have reinvestigated the excited state dynamics of cyclohexa-1,3-diene (CHD) with time-resolved photoelectron spectroscopy and fewest switches surface hopping molecular dynamics based on linear response time-dependent density functional theory after excitation to the lowest lying ππ* (1B) state. The combination of both theory and experiment revealed several new results: First, the dynamics progress on one single excited state surface. After an incubation time of 35 ± 10 fs on the excited state, the dynamics proceed to the ground state in an additional 60 ± 10 fs, either via a conrotatory ring-opening to hexatriene or back to the CHD ground state. Moreover, ring-opening predominantly occurs when the wavepacket crosses the region of strong nonadiabatic coupling with a positive velocity in the bond alternation coordinate. After 100 fs, trajectories remaining in the excited state must return to the CHD ground state. This extra time delay induces a revival of the photoelectron signal and is an experimental confirmation of the previously formulated model of two parallel reaction channels with distinct time constants. Finally, our simulations suggest that after the initially formed cis-Z-cis HT rotamer the trans-Z-trans isomer is formed, before the thermodynamical equilibrium of three possible rotamers is reached after 1 ps.

We present a highly efficient and asymptotically linear-scaling graphic processing unit accelerated seminumerical exact-exchange method (sn-LinK). We go beyond our previous central processing unit-based method (

To investigate the role of tachysterol in the photophysical/photochemical regulation of vitamin D photosynthesis, we studied its electronic absorption properties and excited state dynamics using time-dependent density functional theory (TDDFT), second-order approximate coupled cluster theory (CC2), and non-adiabatic surface hopping molecular dynamics in the gas phase. In excellent agreement with experiments, the simulated electronic spectrum shows a broad absorption band with a remarkably higher extinction coefficient than the other vitamin D photoisomers provitamin D, lumisterol, and previtamin D. The broad band arises from the spectral overlap of four different ground state rotamers. After photoexcitation, the first excited singlet state (S 1 ) decays with a lifetime of 882 fs. The S 1 dynamics is characterized by a strong twisting of the central double bond. In 96% of all trajectories this is followed by unreactive relaxation to the ground state near a conical intersection. The double-bond twisting in the chemically unreactive trajectories induces a strong interconversion between the different rotamers. In 2.3 % of the trajectories we observed [1,5]-sigmatropic hydrogen shift forming the partly deconjugated toxisterol D1. 1.4 % previtamin D formation is observed via hula-twist double bond isomerization. In both reaction channels, we find a strong dependence between photoreactivity and dihedral angle conformation: hydrogen shift only occurs in cEc and cEt rotamers and double bond isomerization occurs mainly in cEc rotamers. Hence, our study confirms the previously formed hypothesis that cEc rotamers are more prone to previtamin D formation than other isomers. In addition, we also observe the formation of a cyclobutene-toxisterol in the hot ground state in 3 trajectories (0.7 %).Due to its large extinction coefficient and mostly unreactive behavior, tachysterol acts mainly as a sun shield suppressing previtamin D formation. Tachysterol shows stronger toxisterol formation than previtamin D and can thus be seen as the major degradation route of vitamin D. Absorption of low energy ultraviolet light by the cEc rotamer can lead to previtamin D formation. In addition the cyclobutene-toxisterol, which possibly reacts thermally to previtamin D, is also preferably formed at long 2 wavelengths. These two mechanisms are consistent with the wavelength dependent photochemistry found in experiments. Our study reinforces a recent hypothesis that tachysterol constitutes a source of previtamin D when only low energy ultraviolet light is available, as it is the case in winter or in the morning and evening hours of the day.3

We introduce tight upper bounds for a variety of integrals appearing in electronic structure theories. These include electronic interaction integrals involving any number of electrons and various integral kernels such as the ubiquitous electron repulsion integrals and the three- and four-electron integrals found in explicitly correlated methods. Our bounds are also applicable to the one-electron potential integrals that appear in great number in quantum mechanical (QM), mixed quantum and molecular mechanical (QM/MM), and semi-numerical methods. The bounds are based on a partitioning of the integration space into balls centered around electronic distributions and their complements. Such a partitioning leads directly to equations for rigorous extents, which we solve for shell pair distributions containing shells of Gaussian basis functions of arbitrary angular momentum. The extents are the first general rigorous formulation we are aware of, as previous definitions are based on the inverse distance operator 1/r12 and typically only rigorous for simple spherical Gaussians. We test our bounds for six different integral kernels found throughout quantum chemistry, including exponential, Gaussian, and complementary error function based forms. We compare to previously developed estimates on the basis of significant integral counts and their usage in both explicitly correlated second-order Møller-Plesset theory (MP2-F12) and density functional theory calculations employing screened Hartree-Fock exchange.

We present a method to predict wavelength-dependent product quantum yields (PQYs) for photochemical reactions and applied it to Z/E-isomerization and several ring-closing reactions of Z-2,5-dimethyl-1,3,5-hexatriene and truncated previtamin D. Using branching ratios from surface hopping molecular dynamics, individual trajectories are correlated with the absorption spectra of their initial structures. The wavelength-dependent PQYs are computed by dividing the average spectrum of the initial structures of the product-forming trajectories by the average spectrum of all initial structures. Accurate absorption spectra are calculated using the correlated ADC(2) method with an implicit solvent. Calculations reproduce the experimentally found trend of increasing six-ring formation and decreasing Z/E-isomerization on the red side of the spectrum. Over all seven reactions studied, the mean absolute error (MAE) between experimental and calculated PQYs (MAE) amounts to 8.1%, and the largest MAE is 18.6%. For four reactions, predicted values agree quantitatively with experiments within 5.6%.

To understand how substituents can be used to increase the quantum yield of photochemical electrocyclic ring-closing of the Z-hexa-1,3,5-triene (HT) photoswitch forming cyclohexadiene (CHD), we investigate the S1 photo dynamics of HT and its derivatives 2,5-dimethyl-HT (DMHT), 2-isopropyl-5-methyl-HT (2,5-IMHT), 1-isopropyl-4-methyl-HT (1,4-IMHT), and 2,5-diisopropyl-HT (DIHT) using time-dependent density functional theory surface hopping dynamics. We report detailed photoproduct distributions, formation mechanisms, branching ratios, and wavelength-dependent product quantum yields. Most products have been confirmed experimentally and include all-trans HT derivatives, cyclopropanes, cyclobutenes, cyclopentene, cyclohexadienes, and bicyclic compounds. Regarding CHD formation, we find that for the 2,5-substituted derivatives DMHT, 2,5-IMHT, and DIHT, the branching ratios increase with increasing size of the substituents. In contrast the branching ratios of the E/Z-isomerization decrease with increasing size of the substituents. Due to steric interactions, increasing the size of the substituents increases the amount of gZg rotamers in the ground state, which are prone to CHD formation and have lower E/Z-isomerization probability. Furthermore, we find [1,4], [1,5], and [1,6]-sigmatropic hydrogen shift reactions occurring at large percentages (5% to 15%); for sterical reasons these reactions stem from tZg conformers. DIHT shows the lowest percentage of side product formation among the 2,5-substituted molecules and highest CHD branching ratio; its CHD quantum yield can be increased up to more than 64%, by excitation of DIHT on the red tail of its absorption spectrum, whereas the Z/E-isomerization is reduced below 5% and side reactions practically vanish. This makes DIHT the best candidate for applications in molecular switches.

We introduce both rigorous and non-rigorous distance-dependent integral estimates for four-center two-electron integrals derived from a distance-including Schwarz-type inequality. The estimates are even easier to implement than our so far most efficient distance-dependent estimates [S. A. Maurer et al., J. Chem. Phys. 136, 144107 (2012)] and, in addition, do not require well-separated charge-distributions. They are also applicable to a wide range of two-electron operators such as those found in explicitly correlated theories and in short-range hybrid density functionals. For two such operators with exponential distance decay [e and erfc(0.11⋅r)/r], the rigorous bound is shown to be much tighter than the standard Schwarz estimate with virtually no error penalty. The non-rigorous estimate gives results very close to an exact screening for these operators and for the long-range 1/r operator, with errors that are completely controllable through the integral screening threshold. In addition, we present an alternative form of our non-rigorous bound that is particularly well-suited for improving the PreLinK method [J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 138, 134114 (2013)] in the context of short-range exchange calculations.

An empirically scaled version of the explicitly correlated F12 correction to second-order Møller–Plesset perturbation theory (MP2-F12) is introduced. The scaling eliminates the need for many of the most costly terms of the F12 correction while reproducing the unscaled explicitly correlated F12 interaction energy correction to a high degree of accuracy. The method requires a single, basis set dependent scaling factor that is determined by fitting to a set of test molecules. We present factors for the cc-pVXZ-F12 (X = D, T, Q) basis set family obtained by minimizing interaction energies of the S66 set of small- to medium-sized molecular complexes and show that our new method can be applied to accurately describe a wide range of systems. Remarkably good explicitly correlated corrections to the interaction energy are obtained for the S22 and L7 test sets, with mean percentage errors for the double-zeta basis of 0.60% for the F12 correction to the interaction energy, 0.05% for the total electron correlation interaction energy, and 0.03% for the total interaction energy, respectively. Additionally, mean interaction energy errors introduced by our new approach are below 0.01 kcal mol−1 for each test set and are thus negligible for second-order perturbation theory based methods. The efficiency of the new method compared to the unscaled F12 correction is shown for all considered systems, with distinct speedups for medium- to large-sized structures.