Fourth Excited State Research Articles

Limits of the harmonic approach for the Morse potential

This paper presents the solution of the Morse potential via the Variational Method using a trial eigenfunction based on the harmonic oscillator and without variational parameters. The first fundamental state and the first nine excited states for the diatomic molecules of hydrogen, lithium hydride, sodium hydride, oxygen, carbon monoxide and silicon monoxide are calculated. The results obtained by the variational method are compared with the values obtained by the exact solution of the same potential in order to establish a percentage error for each energy level of the molecules analyzed and to verify up to which level the chosen trial eigenfunction describes the original system well. That shows that the approximation of the trial eigenfunction is reasonable for the first excited states. From the fourth or fifth excited state, depending on the molecule, the discrepancy no longer reasonable.

Collisional-radiative modeling of shock-heated nitrogen mixtures

A three-temperature collisional-radiative model for shock-heated nitrogen–argon mixtures is developed to facilitate the study of nonequilibrium electronic excitation and ionization behind strong shock waves. Model predictions accurately reproduce measurements of N2 dissociation for mixtures of 2%–10% N2 in argon, with some discrepancies observed for 20% N2 mixtures. Potential causes of the discrepancies are discussed. Net dissociation in mixtures containing 20% N2 is significantly impacted by the dissociation of N2(A), the first excited electronic state of N2, indicating that molecular electronic excitation can affect net dissociation in shock-heated nitrogen flows. The collisional-radiative model successfully predicts the three-stage behavior and induction time observed in concentration measurements of atomic nitrogen in its fourth excited state, the 3s4P level, behind reflected shocks. Mechanisms for the observed behavior are discussed, which deviate from those inferred using a simpler kinetic model. Excited state number density predictions are strongly influenced by the modeling of radiation self-absorption and the inclusion of the measured non-ideal pressure rise. At higher N2 concentrations, the measured data indicate increased efficiency of atomic nitrogen electronic excitation in collisions with N as compared to collisions with N2 and Ar. A global sensitivity analysis of the excited state predictions is then performed, identifying the processes in the kinetic model that most sensitively influence the predicted excited state time history and further clarifying the dominant mechanisms affecting the experimental observables.

Absorption properties and Quantum Confinement of colloidal CdSe quantum dots

We investigate the structural and optical properties of CdSe QDs synthesized by the hot-injection technique. High-resolution transmission electron microscopy (HRTEM) analysis reveal the size-dependent of the CdSe QDs. The first through fourth excited states determined from absorption measurements are compared with calculated quantum size levels in s- and p-symmetry. In particular, featureless absorption peaks of the second and third excited states from the first exciton appear in the differential absorption (DA) spectra. These measurements with quantitative analysis enable the estimate error to be derived from anisotropic properties caused by the crystal field.

Low-lying states of Tl2 and Nh2 with EOM-CC and FSCC methods

Multireference character in the electronic structure of Tl2 and Nh2 is significant and spin–orbit coupling plays an important role in their properties. Single-reference EOM-CCSD and multi-reference IHFSCCSD methods are employed to investigate their low-lying states. Excitation energies with these two methods agree well with each other, while bond lengths with EOM-CCSD are usually too long. Our results on Tl2 agree well with previous MRCI results except that the present bond lengths are generally about 0.1–0.2 Å shorter. As for Nh2, the lowest two states are weakly bounded and the fourth excited state has a stronger chemical bond.

Improved intensities for theγtransitions withEγ>3MeV fromPb*208

$^{208}\mathrm{Pb}$ is a doubly magic nucleus which has been studied extensively by many experiments and nuclear models. Its properties, such as excitation energies, spins, and parities of the ground and excited states are well known. However, some $\ensuremath{\gamma}$ transitions with ${E}_{\ensuremath{\gamma}}g3$ MeV from the excited states to the ground state in $^{208}\mathrm{Pb}$ have never been observed. The intensities of these $\ensuremath{\gamma}$ transitions are important issues for $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay searches because these transitions can make non-negligible background signals depending on their intensities. We conducted a measurement to search for the 3197.7, 3475.1, and 3708.4 keV transitions, which are emitted from the second, third, and fourth excited states in $^{208}\mathrm{Pb}$, respectively. A 2 kg ${\mathrm{ThO}}_{2}$ sample was measured using a 100% relative efficiency high-purity germanium detector for 39.5 days at Y2L, an underground laboratory in Yangyang, Korea. We improved upper limits for intensities of the 3197.7, 3475.1, and 3708.4 keV $\ensuremath{\gamma}$ transitions as $l1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}%, l1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}%$, and $l1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}%$, respectively. These upper limits are at least a factor of 19 better than the previous results.

Three-Dimensional Reference Interaction Site Model Self-Consistent Field Study on the Coordination Structure and Excitation Spectra of Cu(II)-Water Complexes in Aqueous Solution.

The molecular and solvation structures of the hydrated Cu2+ ions and their excitation spectra were investigated using the Kohn-Sham density functional theory (DFT) and the three-dimensional reference interaction site model (3D-RISM) self-consistent field method. Five stable geometrical structures were found to exist in aqueous solution: the distorted octahedral [Cu(H2O)6]2+ in C i and D2 h symmetries, the square pyramidal and trigonal bipyramidal [Cu(H2O)5]2+, and the square planar [Cu(H2O)4]2+. The distorted octahedral structure in the C i symmetry is preferred in [Cu(H2O)6]2+, and the square pyramidal and trigonal bipyramidal [Cu(H2O)5]2+ show almost the same stability. Among these geometries, the six-coordinate complex [Cu(H2O)6]2+ in the C i symmetry had the lowest Helmholtz energy. [Cu(H2O)6]2+ had a distorted octahedral structure, that is, two long axial bonds and four short equatorial bonds. The spatial and radial distribution function analyses for [Cu(H2O)5]2+ and [Cu(H2O)4]2+ showed that [Cu(H2O)5]2+ and [Cu(H2O)4]2+ had one and two solvent water molecules that constituted a distorted octahedron with ligand water distribution. The coordination numbers (CNs) derived from the distribution functions were 5.2-5.4 for [Cu(H2O)5]2+ and 5.3 for [Cu(H2O)4]2+. These results indicated that the Cu2+ ion in an aqueous solution had 5-6 coordination water molecules in the first hydration shell and some structures with different CNs may interchange in the solution. The excitation energies and electronic configurations of low-lying d-d excited states were calculated using the time-dependent DFT with the electric field generated by 3D-RISM. The orbital energies and electronic configurations were in a similar picture to those of the classical crystal field theory because of the highly symmetrical features of all structures. In [Cu(H2O)6]2+, the degeneracies of orbitals were resolved, whereas in [Cu(H2O)5]2+ and [Cu(H2O)4]2+, weak and strong quasi-degeneracies remained. As a result, only the four-coordinate complex generated third and fourth excited states, whereas in other complexes, there were no obvious characters of degeneracies. The resulting excitation energies were in good agreement with the absorption spectra.

New Results for р14N Capture to the 3/2+ Level of the 15O Nucleus at 6.79 MeV

Within the framework of the modified potential cluster model with classification of states according to Young tableaux, the possibility is considered of describing the experimental data on the astrophysical S-factor of radiative p14N capture to the fourth excited state of the 15O nucleus with angular momentum 3/2+ at 6.79 MeV.

Electronic Spectroscopy of Protonated 1‐Aminopyrene in a Cold Ion Trap

In aromatic systems that contain an amino group, there is competition between protonation on a carbon atom of the skeleton and protonation on the amino group. Herein, we studied the photofragmentation of protonated 1-aminopyrene in a cold ion trap and mainly observed the protonated amino tautomer, which led to fragmentation pathways through the loss of H or NH3 groups. Several excited states were assigned, among which the fourth excited state showed broadened bands, thus indicating a fast decay that was attributed to the presence of a πσ* charge-transfer state by comparison of the experimental results with ab initio calculations. We deduced the πσ* transition energies in protonated aromatic amino compounds of increasing size directly from the ionization potentials of the neutral aromatic unsubstituted molecules. Tautomers that were protonated on a carbon atom of the pyrene skeleton were also weakly observed, and we showed that two tautomers that were protonated on a carbon atom of the aromatic ring could be distinguished by using electronic spectroscopy.

Theoretical study of the first electronic state of the FCO2 radical.

Following the successful results for the ground electronic state vibrational levels of the FCO2 radical, the same theoretical approach has been used for predictions of the vibrational levels of the first electronic excited state A (2)A2. This excited electronic state interacts vibronically with the fourth electronic excited state C (2)B1 by normal vibrational modes ν5 and ν6. The intrastate and interstate coupling constants have been determined within the adiabatic quadratic approach in the framework of the Köppler, Domcke, and Cederbaum model Hamiltonian. All ab initio calculations (optimization, potential energies, first and second derivatives) have been performed in two high-level methods (EOMIP-CCSD and UHF-CCSD(T)) using the CFOUR program package. The analytically determined vibronic constant for the ν5 mode has a value of 4061 cm(-1). This causes weak vibronic coupling, implying only the flattening of the potential energy curve, which is in contrast to a double-minimum for the ground electronic state.

Studies on the Way of Obtain C<sub>4</sub>H<sub>8</sub><sup>+ </sup>Small Fragments by the Ring of C<sub>5</sub>H<sub>8</sub>O<sup>+</sup>

Using B3LYP method to obtain the stable configuration of C5H8O+, and is used as the reference configuration. In the 6-31+G (D, P) basis set, we have used CIS method to calculate the structure of cyclopentanone ions excited state and vibration frequencies. In the fourth excited state, the vibration frequency is f=-1856.44 cm-1f=-311.471cm-1 , we analyze The main dissociation to obtain small molecule fragments of C4H8+ approach.

Unprecedented magnetic relaxation via the fourth excited state in low-coordinate lanthanide single-ion magnets: a theoretical perspective.

Four low-coordinate SIMs have been studied to probe their relaxation dynamics using ab initio calculations. Our calculations reveal that both the symmetry and the equatorial ligand field play a key role in controlling the barrier heights in three-coordinate [Ln(III)(NSiMe3)3] complexes (Ln = Dy/Er). This study reveals an unprecedented blockade of magnetization up to three excited states for the Er(III) complex.

Three-Dimensional Reference Interaction Site Model Self-Consistent Field Study of the Electronic Structure of [Cr(H2O)6]3+ in Aqueous Solution

The three-dimensional reference interaction-site model self-consistent-field (3D-RISM-SCF) method was applied to the electronic structure of hexahydrated chromium trication [Cr(H2O)6](3+) in aqueous solution. The 3D distribution around [Cr(H2O)6](3+) showed 12 maximum density points arising from hydrogen bonds, as well as eight local maximum points at the hollow sites, in the second hydration shell. The 3D distribution function also indicated 20 local maximum sites in the third hydration shell. The low-lying excited states of vertical transitions were computed using time-dependent density functional theory (TD-DFT), including the electric field from the solvent. The electronic configurations and excitation energies calculated using DFT and 3D-RISM-SCF were very similar, although the orbital energies involved in the transition were rather different. The two lowest excited states (1(4)T and 2(4)T) were roughly assigned to the d-d transitions, and the third and fourth excited states (3(4)T and 4(4)T) were assigned to ligand-to-metal charge-transfer transitions. The computed excited energies were in good agreement with the experimental values.

Controlling the Photoreactivity of the Photoactive Yellow Protein Chromophore by Substituting at the p-Coumaric Acid Group

We have performed ab initio CASSCF, CASPT2, and EOM-CCSD calculations on doubly deprotonated p-coumaric acid (pCA2−), the chromophore precursor of the photoactive yellow protein. The results of the calculations demonstrate that pCA2− can undergo only photoisomerization of the double bond. In contrast, the chromophore derivative with the acid replaced by a ketone (p-hydroxybenzylidene acetone, pCK−) undergoes both single- and double-bond photoisomerization, with the single-bond relaxation channel more favorable than the double-bond channel. The substitution alters the nature of the first excited states and the associated potential energy landscape. The calculations show that the electronic nature of the first two (π,π*) excited states are interchanged in vacuo due to the substitution. In pCK−, the first excited state is a charge-transfer (CT π,π*) state, in which the negative charge has migrated from the phenolate ring onto the alkene tail of the chromophore, whereas the locally excited (LE π,π*) state, in which the excitation involves the orbitals on the phenol ring, lies higher in energy and is the fourth excited state. In pCA2−, the CT state is higher in energy due the presence of a negative charge on the tail of the chromophore, and the first excited state is the LE state. In isolated pCA2−, there is a 68 kJ/mol barrier for double-bond photoisomerization on the potential energy surface of this LE state. In water, however, hydrogen bonding with water molecules reduces this barrier to 9 kJ/mol. The barrier separates the local trans minimum near the Franck−Condon region from the global minimum on the excited-state potential energy surface. The lowest energy conical intersection was located near this minimum. In contrast to pCK−, single-bond isomerization is highly unfavorable both in the LE and CT states of pCA2−. These results demonstrate that pCA2− can only decay efficiently in water and exclusively by double-bond photoisomerization. These findings provide a rationale for the experimental observations that pCA2− has both a longer excited-state lifetime and a higher isomerization quantum yield than pCK−.

Dissociation Channels of c-C4F8 to CF2 Radical in Reactive Plasma

It has been generally assumed that octafluorocyclobutane (c-C4F8) is mainly decomposed to CF2 via C2F4 in etching process plasma. However, the detailed mechanism for the dissociations is yet ambiguous. In this paper we have calculated the probable dissociation pathways by using ab initio molecular orbital method. The results show that c-C4F8 is dissociated via the first triplet excited state T1(3A2), the fourth triplet excited state T4(32E) and the fourth singlet excited state S4(12E). One of the degenerate excited states of T4 and S4 is constituted by antibonding combination of two π bonding orbital of C2F4. T1 state is constituted by antibonding combination of b1u antibonding σ orbital of C2F4. Therefore, in the case of the dissociation via S4 and T4 excited states c-C4F8 may dissociate to two C2F4, and in the case of the dissociation via T1 excited state c-C4F8 may dissociate to four CF2 radicals. It is also found that C3F5+ ion observed as the main peak in c-C4F8 process plasma is produced by electron collision with the slightly larger energy than the ionization threshold value. The main dissociation path of C2F4 is a vertical electron attachment. However, it is also found that dissociation pathways via 1B2g, 3B1u, and 3B2g excited states are very important and should not be ignored.

Ultracold experiments strike universal physics—again

Vitaly Efimov predicted in 1970 [1] that three particles can have an infinity of bound states even when no two of the three are separately bound together. The existence of even a single state so delicate is surprising, but the presence of an infinite sequence of them is doubly so. Even more confounding to our intuition is the fact that making the underlying interactions between the three particles stronger decreases the number of threebody bound states from infinity to a finite value. We normally think, of course, that deepening a potential leads to more bound states, not fewer. Besides a parameter that fixes the short-range behavior of the three bodies, the properties of these Efimov states (as they have come to be called) are universal and characterized by geometric scaling. For instance, given the energy of a bound Efimov three-boson state, you know that the next state is 515 times more weakly bound, and that the state after that is another 515 times more weakly bound, and so on. The spatial size of the states grows by factors of 22.7—the fourth excited state is already at least micron-sized! Geometric scaling is the signature of Efimov states in all low-energy observables.

On the mechanism of formation of excited states of the 8Be nucleus in the reaction 12C(γ, 3α)

The reaction 12C(γ, 3α) was studied with the aid of a diffusion chamber placed in a magnetic field, filled with a methane-helium mixture, and irradiated with bremsstrahlung photons of endpoint energy 150 MeV. The total reaction cross section was measured in the energy range Eγ < 40 MeV. The ground state; the first, second, and unseparated third and fourth excited states; and highly excited states (in the range 19.9 < Ex < 25.2 MeV) of the 8Be nucleus manifested themselves in the distribution of events with respect to the energy of the relative motion of two alpha particles. A resonance that is characterized by the energy of E0 = 0.72 MeV and the width of Γ = 0.80 MeV and which was identified as a ghost anomaly was found between the ground state and the first excited state. Partial cross sections were measured for various channels. Excited states are formed in narrow photon-energy intervals, and their partial cross sections are of a resonance shape. It is found that the energy corresponding to the maximum of the partial cross section for the ith level, Emi, and the excitation energy of the next level, E0i+1, are correlated: Emi = E0i+1 + ɛ, where ɛ is the reaction threshold. The results are qualitatively explained on the basis of a model that assumes photon absorption by an alpha-particle pair.

Vibronic induced one- and two-photon absorption in a charge-transfer stilbene derivate

Both the electronic and the vibronic contributions to one- and two-photon absorption of a D-pi-D charge-transfer molecule (4-dimethylamino-4'-methyl-trans stilbene) are studied by means of density functional response theory combined with a linear coupling model. Vibronic profiles of the first four excited states are fully explored. The dominating vibrational modes for both Franck-Condon and Herzberg-Teller contributions are identified. The Franck-Condon contribution dominates the spectra of first, second, and fourth excited states. The Herzberg-Teller contribution is on the other hand of comparable size for the third excited state, where its inclusion leads to a blueshift with respect to the vertical transition. A similar vibronic coupling behavior is found for both one- and two-photon absorptions.

Quantum states of a hydrogen atom adsorbed onCu(100)and (110) surfaces

Quantum states of a hydrogen atom adsorbed on $\mathrm{Cu}(100)$ and $\mathrm{Cu}(110)$ are studied theoretically. In calculating eigenenergies and wave functions of hydrogen atom motion, three-dimensional adiabatic potential energy surfaces (PESs) are constructed within density functional theory and the Schr\odinger equation for hydrogen atom motion on the PESs is solved by the variation method. The wave function on $\mathrm{Cu}(100)$ indicates a localized mode on the hollow (HL) site at the ground state. Wave functions of the first few excited states indicate vibrational modes on the HL site and suggest migration from an HL site to a neighboring HL site over the bridge (BR) site. In the case of $\mathrm{Cu}(110)$, the ground state wave function is spread from the short bridge (SB) site and to the pseudothreefold (PT) site. The first few excited states are vibrational modes centered at the SB and long bridge (LB) sites. The excited state wave function of the hydrogen atom motion on $\mathrm{Cu}(110)$ show isotope effects as follows. The fourth excited state wave function for the H atom motion shows a localized character on the LB site, and those for D and T atom motion show vibrational modes parallel to the surface. On the other hand, the fifth excited state wave functions for D and T atom motion show localized characters on the LB site and that for H atom motion shows a vibrational mode parallel to the surface. Our calculated eigenenergies of the hydrogen atom motion in excited states on $\mathrm{Cu}(100)$ and $\mathrm{Cu}(110)$ are fairly in agreement with their corresponding experimental findings.

Spectral and temporal resolution of recombination from multiple excitation states in modulation-doped AlGaN∕GaN multiple quantum well heterostructures

Time-resolved photoluminescence measurements of carrier lifetimes in modulation-doped (100Å)AlxGa1−xN∕(100Å)GaN multiple quantum well heterostructures are reported. The photoluminescence (PL) spectrum exhibits several lines associated with recombination of carriers from multiple excited electron states to the hole ground state. The PL decay times associated with ground state recombination, e0h0, are found to be much longer than the inverse repetition rate of our system (20μs) and estimated to be 9 ms. The experimental lifetimes associated with carrier recombination from excited states vary between 4μs for the first excited state, e1h0, and 4.5 ns for the fourth excited state, e4h0. These lifetimes are in very good agreement with a self-consistent calculation of radiative recombination lifetimes which takes into account piezoelectric and spontaneous polarization. The significant differences in recombination lifetimes are the result of the large built-in electric field in the wells (0.5MV∕cm).

The influence of symmetries of the substituted donor and acceptor on two-photon absorption cross sections of trans-stilbene derivatives

We have designed a series of trans-stilbene derivatives with different arrangement of the substituents and studied their one-photon and two-photon absorption properties by using the response theory methods at HF level. The calculations show that these molecules have strong two-photon absorption cross sections. In the visible light region, the maximum two-photon absorption cross section for molecules with asymmentric substitution of the donor and acceptor occurs in the first excited state, while for the symmetric substitution cases it occurs in the fourth excited state. The asymmetry-substituted molecules have a larger two-photon absorption cross section than the symmetry substituted molecules, indicating that the effect of the different kinds of substituents on the two-photon absorption of molecules is related to the property of theiry π-centers. The charge-transfer process for the charge-transfer states was visualized in order to understand their maximal two-photon absorption cross sections.