tions to the RS-based first-order perturbative **excitation** **energies** are significant (more than − 0.01 eV) and strongly reduce the errors. As µ increases, the corrections coming from the additional term in Eq. (19) change sign but are still efficient to reduce the errors. For sufficiently large µ, in comparison to the zeroth-order **excitation** **energies** and to the zeroth+first-order RS **excitation** **energies**, the zeroth+first-order GL ex- citation **energies** systematically converge faster with respect to the range-separation parameter to the physical **excitation** **energies**: a 1 millihartree accuracy is reached for µ larger than 1.2 bohr −1 , while values of 3 to 4 bohr −1 are necessary for the zeroth-order curves. However, near µ = 0, the first-order GL correction does not always improve the zeroth-order **excitation** energy (see the 1 1 S → 1 1 P transition).

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state—see the bottom part of Figure 3. Again, the improvement is systematic. The triplet extrap- olated energy shows a monotonic behavior with respect to µ, whereas the singlet energy shows a slight bump at 0.8 bohr −1 . However, all ex- trapolated **excitation** **energies** converge faster than their unextrapolated counterparts. Extrapolation works remarkably well, reducing errors to less than 5 millihartree with µ ≈ 0.6 bohr −1 , compared with 2 bohr −1 without extrapolation. In particular, ex- trapolation allows us to describe double and sin- gle **excitation** **energies** equally well. In this case, one should note that the second-order scheme does

FRS (FRagment Separator -GSI) at 1, 0.8, 0.5 and 0.3 GeV with an specific setup, pro- viding high accuracy measurements of the cross section values. We compare the results obtained in this experiment, with several calculations performed with the intra-nuclear cascade model (INCL v4.1) coupled to de-**excitation** code (ABLAv3p), according to two diﬀerent models describing fission process at high-**excitation** **energies**: statistical model of Bohr and Wheeler and the dynamical description of the fission process. The compar- ison with data of previous experiments is also discussed in order to address the existing discrepancies with this new results.

Numerous experiments related to the nuclear fission process [1,2], in particular those aiming for discovering new superheavy elements [3-5], require practical and reliable numerical modeling of fission dynamics at low **excitation** **energies**. The most important physical quantity characterizing the fission process, although not ob- servable, is the fission rate which is by definition

We explore the possibility of calculating electronic excited states by using perturbation the- ory along a range-separated adiabatic connection. Starting from the **energies** of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straightforward perturbation theory, and an extension of the G¨ orling–Levy one that has the advantage of keeping the ground-state density constant at each order in the perturba- tion. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the hydrogene molecule. The first-order correction within this perturbation theory improves significantly the total ground- and excited-state **energies** of the different systems. However, the **excitation** **energies** mostly deteriorate with respect to the zeroth-order ones, which may be ex- plained by the fact that the ionization energy is no longer correct for all interaction strengths. The second (G¨ orling–Levy) variant of the perturbation theory should improve these results but has not been tested yet along the range-separated adiabatic connection.

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derived from common density functionals is a major problem, because it causes inaccurate Rydberg **excitation** **energies** and erroneous fractional charges in dissociating molecules. An efficient method to correct the shape of the exchange-correlation potential in the asymptotic regions was proposed by Gaiduk et al. [A. P. Gaiduk, D. S. Firaha, and V. N. Staroverov, Phys. Rev. Lett. 108, 253005 (2012)]. In that method, the exchange- correlation potential of an auxiliary system with a fractionally occupied frontier orbital is used to construct a model potential for the neutral system of interest. In this thesis, we investigate a method to eliminate unphysical partial charges on atoms in dissociating polar molecules via the use of the fractional occupation technique. The method proves successful not only for enforcing correct integer charges in the dissociation limit, but also for predicting how atomic charges change at intermediate interatomic separations. We also test the hypothesis that a fractionally charged system with an integral number of electrons but fractional nuclear charge may be used to correct the exchange-correlation potential in order to obtain more accurate Rydberg **excitation** **energies**. Our findings show that, although the model potentials generated in this way give rise to some im- provements, the optimal nuclear charge to be added depends on the system. In contrast, the advantage of the method of fractional orbital occupations is that the parameter re- quired to correct **excitation** **energies** is system-independent.

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Second, contrary to the ∆SCF method CIS calculates all singly excited states si- multaneously. The formulation of the ∆SCF method only allows for one excited state to be calculated at a time and requires separate subsequent calculations to calculate other states. This property of the CIS method is not only computationally convenient but also gives valuable information about the vertical ordering of states. The CIS method can calculate any number of excited states above the ground state depending on the amount of virtual orbitals that are calculated from the initial Hartree-Fock reference wavefunction. The calculation of these states at any state’s given equilib- rium bond distance allows the user to see how all of the other states are ordered and are able to compare vertical **excitation** **energies** of all states at once. This is also a boon to the user because many points on different excited state potential energy surfaces can be calculated and compared simultaneouly. This is all contrary to the ∆SCF method where only single potential energy surface points and single **excitation** **energies** can be evaluated with each calculation.

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actions of heavy nuclei. The double diﬀerential cross sec- tions of the reactions include the contribution of quasi- elastic and inelastic elementary processes which are de- scribed in terms of the exchange of virtual pions. The in- elastic channel includes processes where the resonances are excited both in the target and in the projectile. Our re- sults conﬁrm that the position of the Δ peak is insensitive to targets with mass number A ≥ 12, and show that the origin of its shift towards low **excitation** **energies**, with re- spect to its position in reactions with a proton target, can be easily explained in terms of the superposition of the diﬀerent **excitation** mechanisms contributing to the reac- tion. We want to point out that our model is being used in the analysis and interpretation of the results of several isobaric charge-exchange inclusive reactions recently per- formed with the FRS at GSI using stable and unstable Sn projectiles on diﬀerent targets [11, 12]. The results of this analysis are still under evaluation and, therefore, they have not been discussed here.

vibrational frequencies compared to the spin mixed state. Spin-purification has the greatest effect on the **excitation** **energies**, which are much closer to experiment but remain consistently too low and less accurate than TDDFT. The computed **excitation** **energies** also show a greater sensitivity to the choice of exchange-correlation functional than TDDFT. The predicted structures from eDFT are of a similar accuracy to TDDFT, and spin-purification does correct the few significantly larger errors found with eDFT SM . For calculated scaled and harmonic frequencies, the values from eDFT SP are found to be closer to experiment than for TDDFT, although spin-purification can lead to different normal modes. Anharmonic eDFT frequencies provide accurate vibrational frequencies for the majority modes for both eDFT SM and eDFT SP . Consequently, eDFT represents a computationally inexpensive approach that provides an alternative to TDDFT that can be applied to study the properties and dynamics of electronically excited states of large molecules .

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The average neutron excess of the ﬁssion fragments, obtained in Ref. [13], is displayed as a function of the atomic number of the ﬁssioning nuclei in Fig. 2 for the reaction 208 Pb + p at 500 A MeV. In the ﬁgure, we also com- pare the neutron excess with our previous model calculations. First, the average neutron excess is compared with a calculation assuming the saddle- to-scission statistical time τ ssc 0 (long-dashed line). As can be observed, this calculation clearly overestimates the neutron excess for the lightest ﬁssion- ing systems. This overestimation indicates the need for dissipation at high **excitation** **energies** where the statistical evaporation time is comparable to the time needed by the ﬁssioning nucleus to descend from the saddle point to scission. Therefore, we also compare the data with dissipative calcula- tions based on Eq. 1, assuming a reduced dissipation parameter β of 4.5 × 10 21 s −1 (short-dashed line), 6.5 × 10 21 s −1 (solid line), and 18 × 10 21 (dot-long-dashed line) s −1 . As can be seen in the ﬁgure, the calculation considering a reduced dissipation parameter of 4.5 × 10 21 s −1 (short-dashed line) or 6.5 × 10 21 s −1 (solid line) can describe the average neutron excess for all the ﬁssioning systems. These results could indicate that the dissi- pation parameter does not depend on deformation because, in our previous works, we have determined a dissipation parameter of (4 . 5 ± 1 . 0) × 10 21 s −1 at small deformations [14, 15].

neutron-rich even-even N > 82 tin isotopes with A = 134 - 140, by employing realistic two-body matrix elements of the interaction and empirical SP **energies** as well as ef- fective neutron charge. Then, we have reported **excitation** **energies** and electromagnetic properties of 130 Te obtained within a more consistent calculation, with a completely microscopic Hamiltonian and e ff ective transition operators derived by using the same framework of the e ff ective shell- model Hamiltonian. In latter case, our aim was to assess the predictive power of our approach, without introducing any adjustable parameters, in order to make predictions for still unknown quantities, as the nuclear matrix element involved in the neutrinoless double-β decay.

Tables 8.10 and 8.9 compare the CAS ground state energy, the ground state dipole moment and the vertical **excitation** **energies** for planar and nonplanar 1H-2-keto 4-amino cytosine respectively, calculated with 16 states and with the active space consisting of 14 electrons distributed over 10 orbitals, (14,10). For the nonplanar molecule the CI calculations with the cc-pVDZ basis set were not converged and were therefore not included in table 8.9. In table 8.10 are also presented the excita- tion **energies** obtained by experiment and from calculations with different methods. The first singlet **excitation** has π → π ∗ character. The exception is the result ob- tained using the 6-31G basis set, where the first singlet **excitation** is n → π ∗ (see table 8.10). These results are different to those of uracil where the first singlet ex- cited state is n → π ∗ (see table 8.3). The first two triplet excited states are of type π → π ∗ . Here also, the character of the excitations is noticeably different from the case of uracil, where the first triplet excited state is π → π ∗ , but the second triplet excited state is n → π ∗ (see table 8.3).

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The RI approximation has been extensively used in connection with CC2 molecular properties [56, 57, 58, 59, 60, 61, 61, 62, 63, 64, 65], but has also been used in connection with the coupled perturbed Kohn–Sham equations[66]. It has also been used in TD-DFT in connection with **excitation** **energies**, excited state gradients and frequency-dependent optical rotation calculations [67, 68, 69, 70, 71]. Density fitting can also be applied for the efficient calculation of nuclear magnetic resonance shielding tensors [72, 73]. Ref. 67 and 70 concluded that the auxiliary basis sets developed for ground-state calculations are sufficient for most TD-DFT applications, although in some cases additional diffuse basis functions must be included. Ref. 70 reported that the total computational effort for excited-state optimizations is reduced by at least a factor of 4-6 by the RI-J approximation, with corresponding RI-J errors of 0.01-0.02 eV. The RI-J errors in optimized bond lengths and angles amounted to less then 0.5 pm and 1 degree, respectively. These deviations are usually much smaller than errors due to the incompleteness of the one-particle basis set.

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protonated methicillin lactim-enol form (3) appears to be more stable. All cations are solvated to form hydrogen bonds with the polar solvents which would affect the position of the equilibrium. As per electron **excitation** **energies** (∆E) (in eV), it is observed the reactivity is decreased in the order of 6 > 3 > 5 > 4 > 2 > 1. It is confirmed that methicillin (1) is more stable than its lactim-enol form (2). The spatial arrangement of atoms in a molecule is considered to study the conformations of methicillin (1), and its methicillin lactim-enol form (2), mono-protonated forms (3 & 4), di-protonated form (5) and anion (6) with a view to investigate molecular deformations. These can exist in anti- or syn- conformation, according to the position of atoms. In this context, the change in energy content of the protonation may depend on the changes in the parameters of dihedral angles. Fully optimized AM1 calculations scrutinize only the main data of bond lengths (Table-II) and dihedral angles (Table-III) of molecules (1 to 6) for the sake of simplicity.

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FIG 1. (a) Sketch of the device and circuit diagram. (b) I-V-curves in the dark and under cw illumination with a LED emitting photons with energy of 2 eV. The arrows indicate the sweep cycle directions. (c) Conductance versus pulse number for pulsed optical **excitation** with photon **energies** of 2 eV, pulse widths of 10 µs, and different light powers. The bias voltage during illumination is -1.8 V. (d) Conductance versus pulse number for pulsed optical **excitation** with photon **energies** of 2 eV, powers of 44 µW, and different pulse widths. No bias voltage is applied during illumination. (e),(f) Sketch of the conduction (CB) and valence (VB) band profiles and the electron-hole dynamics for bias voltages of -1.8 V (e) and 0 V (f).

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The “classical” actinometry approach then enabled to quantify reactive species densities by deliberately adding a suitable tracer noble gas and observing the ratio of both the tracer gas emission and the optical emission of the reactive species. The reactive species density can be determined under the assumption that the involved excited states are of similar **excitation** energy and solely populated through direct electron-impact **excitation** from the corresponding atomic ground state. 5 The time averaged emission intensity hIi rf from one of the states is given by hIi rf ¼ h a ik hk e n e i rf n 0 .

It is well-known that the mass (charge) distributions of the neutron induced ﬁssion of pre-actinides are symmet- ric, while of the nuclei U–Cf and Ac–Pa near the line of stability are asymmetric with two and three maxima, re- spectively [1, 2]. For the neutron-deﬁcient actinides Ac– U, the symmetric mode is the most predominant. How- ever, in neutron-deﬁcient 180 Hg the asymmetric mass dis- tribution of ﬁssion fragments was unexpectedly observed in the recent experiment [1, 3]. Despite six decades of the experimental and theoretical research there is still no satisfactory understanding why the transition from a sym- metric to an asymmetric ﬁssion occurs with increasing mass or decreasing **excitation** energy of the ﬁssioning nu- cleus. In Ref. [4], it was suggested that the competi- tion between symmetric and asymmetric ﬁssion is related to the shell eﬀects in the deformed ﬁssioning nucleus. With increasing energy the shell eﬀects wash out, leav- ing the nucleus with a dominant symmetric mode of ﬁs- sion. However, the new experimental data of ﬁssion of

Another crucial factor is the initial state, i.e. which BChl molecules are excited in the begin- ning. We considered different initial conditions, namely when the **excitation** is localized either on BChl 1, 6, or 8. This choice of the initial state is motivated by the assumption that BChl 1, 6, or 8 have the highest probability to obtain the excita- tion from the chlorosome antenna structure. Re- markably, when initially only BChl 8 is excited, it was found that a slow exponential-like transfer away from BChl 8 takes place. This is in con- trast to the oscillations found when starting on BChl 1 and the faster transfer away from BChl 1 or 6. These oscillations have been the subject of study of many research groups, both theoretically and experimentally. Ultrafast experiments where BChl 8 is present as well might reveal this strong difference in the energy transfer dynamics away from it. Furthermore, we found that the influence of variations of different parameters on the trans- fer strongly depends on the initial state. Here, the parameters we varied include electronic ener- gies, coupling **energies** between BChl molecules, or the coupling to the environment. Because of this strong dependence on the initial condition, in further investigations it would be important to get more detailed information about the arrangement of the FMO w.r.t. the baseplate and the chloro- somes and learn more about the transfer of exci- tation from the chlorosomes to the FMO complex. Let us briefly compare our findings with those of Refs., 1,6 from which the couplings and ener- gies of the BChls were taken. In Ref. 6 Olbrich et. al. found an even slower decay of the excita-

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Under adequate conditions, cavity polaritons form a macroscopic coherent quantum state, known as polariton con- densate. Compared to Wannier-Mott excitons in inorganic semiconductors, the localized Frenkel excitons in organic emitter materials show weaker interaction with each other but stronger coupling to light, which recently enabled the first realization of a polariton condensate at room temperature. However, this required ultrafast optical pumping, which limits the applications of organic polariton condensates. We demonstrate room temperature po- lariton condensates of cavity polaritons in simple laminated microcavities filled with biologically produced enhanced green fluorescent protein (eGFP). The unique molecular structure of eGFP prevents exciton annihilation even at high **excitation** densities, thus facilitating polariton condensation under conventional nanosecond pumping. Condensation is clearly evidenced by a distinct threshold, an interaction-induced blueshift of the condensate, long- range coherence, and the presence of a second threshold at higher **excitation** density that is associated with the onset of photon lasing.

Experimentally, only little is known about the QCD phase diagram. The comparison of the mea- sured yields of particles and antiparticles to the results of thermal model calculations provides a so called freeze-out temperature as function of baryon chemical potential [7, 8]. This temperature is measured at a late stage of the collision, when the produced particles cease to interact, and the density has dropped well below saturation density. However, for LHC and top RHIC **energies**, the freeze-out temperature coincides with the pseudo-critical temperature predicted by QCD, indicating that freeze- out and hadronization might happen simultaneously. The mission of heavy-ion experiments at lower beam **energies** includes the search for the landmarks in the QCD phase diagram, such as the critical point and a first order phase transition. Another fundamental ingredient for our understanding of nu-

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