Orbit-orbit relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of H(2)

We report the derivation of the orbit-orbit relativistic correction for calculating pure vibrational states of diatomic molecular systems with sigma electrons within the framework that does not assume the Born-Oppenheimer (BO) approximation. The correction is calculated as the expectation value of the orbit-orbit interaction operator with the non-BO wave function expressed in terms of explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. With that we can now calculate the complete relativistic correction of the order of alpha(2) (where alpha=1/c). The new algorithm is applied to determine the full set of the rotationless vibrational levels and the corresponding transition frequencies of the H(2) molecule. The results are compared with the previous calculations, as well as with the frequencies obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in alpha to further improve the agreement between the theory and the experiment.     

The lowest singlet states of octatetraene revisited

The two lowest excited singlet states of all-trans-1,3,5,7-octatetraene, 2?(1)A(-)(g) and 1?(1)B(+)(u), are studied by means of high level ab initio methods computing the vertical and adiabatic excitation energies for both states and the vertical emission energy for the 1 (1)A(g)(-)←2?(1)A(-)(g) transition. The results confirm the known assignment of two energies, the 2?(1)A(-)(g) adiabatic excitation energy and the 2?(1)A(-)(g) vertical emission energy, for which well defined experimental values are available, with an excellent agreement between theory and experiment. In the experimental absorption spectrum, the maximum of the band describing the 1?(1)B(+)(u)←1?(1)A(g)(-) excitation is the first peak and it has been assigned to the (0-0) vibrational transition, but in literature it is normally compared with the theoretical vertical excitation energy. This comparison has been questioned in the past, but a conclusive demonstration of its lack of foundation has not been given. The analysis reported here, while confirming the assignment of the highest peak in the experimental spectrum to the (0-0) adiabatic transition, indicates that it cannot be used as a reference for the vertical excitation energy. The theoretical vertical excitation energies for the 2?(1)A(-)(g) and 1?(1)B(+)(u) states are found to be almost degenerate, with a value, ? 4.8 eV, higher than that normally accepted in the literature, 4.4 eV. The motivations which have induced in the past other authors to consider this a correct value are discussed and the origin of their feebleness are analyzed.     

Accurate values for the nonrelativistic energies of the lowest singlet and triplet S-states of the4He-Isotop

Accurate lower and upper bounds for the nonrelativistic lowest energies¹ E ₀ and³ E ₀ of the singlet and triplet-system of the⁴He-Isotop are calculated with the linearized method of variance minimization. The same was done for¹ E ₁ the energy of the first excitedS-state 2¹ S. The results especially for¹ E ₀ and³ E ₀ in a.u. are −2.9033076997₅ ≤¹ E ₀ ≤ −2.9033076921₈ −2.1749324263₇ ≤³ E ₀ ≤ −2.1749324245₉ i.e. the values are determined with an absolute error smaller than 0.00167 cm⁻¹ for¹ E ₀ and 0.00039 cm⁻¹ for³ E ₀.     

Resonance CARS spectra of the lowest excited singlet states of rhodamines

The resonance CARS spectra of the S₁ states of rhodamine 6G, rhodamine B and sulforhodamine were obtained by choosing ω₁ resonant with the S₁ ← S₀ and S₃ ← S₁ transitions simultaneously and by varying the laser beam power density of ω₁ or ω₂. The vibrational frequencies for the S₀ and S₁ states are similar, implying that the structure of the S₁ state is not distorted significantly.     

Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H2

The Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the H2 using the perturbation theory and very accurate variational wave functions obtained without assuming the Born-Oppenheimer (BO) approximation. Expansions in terms of explicitly correlated Gaussians with premultipliers in the form of even powers of the internuclear distance were used for the wave functions. With the inclusion of the two relativistic corrections to the non-BO energies the transition energies for the highest states agree more with the experimental results.     

Relativistic corrections in a series of helium excited states

Relativistic corrections to order (υ/c)² are applied to the helium excited states 2 ^1,3P, 3 ^1,3D,…, 8 ^1,3K. Simple correlated open-shell wavefunctions are employed and the Breit operators H₁ through H₅ treated as perturbations. Account is also taken of mass polarization and lowest-order one electron Lamb shift. The energies thus calculated agree with experiment to within 2.2 cm^?1 or better.     

Spectrometric evidence ford-orbital participation in the lowest excited singlet states of naphthalenethiols

Tellurium can be determined polarographically in the range 10^?5–10^?8M by means of the Te⁰_ads→Te^2- reduction in 1M perchloric acid as supporting electrolyte. Pulse polarography, a.c. polarography and linear sweep cyclic voltammetry can be used to determine tellurium in the p.p.b. range. Copper(II), arsenic(III) and selenium(IV) interfere, but the interferences can be overcome by a standard addition method.     

Doubly excited Rydberg states of He I and Ba I

The Auger decay widths of doubly-excited Rydberg states of He I and Ba I have been calculated by the multi-configuration Hartree-Fock procedure. The configuration mixing is crucial in obtaining the correct widths, while the energies seem to be relatively less sensitive to mixing. The usual mixing procedure is often unstable for doubly excited states and careful selection of configurations is required. An improved procedure for selecting the states for mixing is formulated, which seems to stabilize the calculation of both the energies and widths, with small numbers of configurations which are mixed. We apply the recipe to a selected set of doubly excited states of He and Ba. The long standing discrepancies in the widths for the series 7sns, 7snd, 8sns, and 8snd of Ba I withn > 11 may be explained by this procedure, except for the 7snd series. The calculated widths for the 7snd series are larger than the experimental values by a factor of 10–20. The difficulties of treating the states with both electrons in higher Rydberg orbitals are discussed.     

Ab initio study of small He cluster ions He n + ,n=2, 3, 4, 5, and low-lying Rydberg states of He4

SCF and CEPA calculations are applied to study the structure of small He cluster ions, He _n ⁺ ,n=2, 3, 4, 5 and some low-lying Rydberg states of He₄. The effect of electron correlation upon the equilibrium structures and binding energies is discussed. He ₃ ⁺ has a linear symmetric equilibrium geometry with a bond length of 2.35a ₀ and a binding energyD _e =0.165 eV with respect to He ₂ ⁺ +He (experimentally:D ₀=0.17 eV which corresponds toD _e ≈0.20 eV). He ₄ ⁺ is a very floppy molecular ion with several energetically very similar geometrical configurations. Our CEPA calculations yield a T-shaped form with a He ₃ ⁺ centre (R _e = 2.35a ₀) and one inductively bound He atom (4.39a ₀ from the central He atom of He ₃ ⁺ ) as equilibrium structure. Its binding energy with respect to He ₃ ⁺ +He is 0.031 eV. A linear symmetric configuration consisting of a He ₂ ⁺ centre with a bond length of 2.10a ₀ and two inductively bound He atoms (4.20a ₀ from the centre of He ₂ ⁺ ) is only 0.02–0.03 eV higher in energy. We expect that in larger He cluster ions structures with He ₂ ⁺ and He ₃ ⁺ centres andn?2 orn?3 inductively bound He atoms have nearly the same energies. In He₄ a low-lying metastable Rydberg state (³ Π symmetry for linear He ₄ ^* ,³ B ₁ for the T-shaped form) exists which is slightly stronger bound with respect to He ₃ ^* +He than the corresponding ion.     

Photophysical properties of the lowest excited singlet and triplet states of thio- and seleno-psoralens

The decay processes of the lowest excited singlet and triplet states of five heteropsoralens (HPS) were investigated by steady-state and shift-phase fluorometry and by laser-flash photolysis in different solvents. The emission spectra of HPS are detectable only in trifluoroethanol (TFE), where fluorescence lifetimes (τ_F) and quantum yields (φ_F) were measured. The triplet lifetimes (τ_T), triplet (φ_T) and singlet-oxygen production (φ_Δ) quantum yields were determined in benzene, ethanol and TFE by laser-flash photolysis. Semiempirical (INDO/1-CI) calculations allowed the nature of the lowest excited singlet and triplet states and transition probabilities to be obtained. Theoretical and experimental results indicate that the two lowest excited singlet states S₁ and S₂ of HPS are close-lying and different in nature (π,π* and n,π*). The "proximity effect" between these two states controls the photophysical properties of HPS as it does for the other furocoumarins. However, HPS have a peculiar behavior with respect to the related compounds because they are fluorescent and have, in three cases, detectable intersystem crossing only in TFE. This behavior can be tentatively explained by a different energy gap and/or order between the S₁ and S₂ states.     

The lowest excited singlet states of 1-arylbutadienes: photochemical implications

PPP calculations on 1-arylbutadienes predict a forbidden transition slightly below the first allowed transition. The two lowest excited singlet states have different calculated charge densities, implying different types of photochemical reaction.     

A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol

Summary The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm^–1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (2¹ E_2g) is the highest valence * state predicted by elementary -electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53–7.84 eV (63 300 cm^–1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.     

Finite element investigation of the ground states of the helium trimers 4He3 and 4He2–3He

A three‐dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers ⁴He₃ and ⁴He₂–³He. Three different He–He interaction potentials of hard‐core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Influence of excited state aromaticity in the lowest excited singlet states of fulvene derivatives

The absorption spectra and excited state dipole moments of four differently substituted fulvenes have been investigated both experimentally and computationally. The results reveal that the excited state dipole moment of fulvenes reverses in the first excited singlet state when compared to the ground state. The oppositely polarized electron density distributions, which dominate the ground state and the first excited singlet state of fulvenes, respectively, reflect the reversed π-electron counting rules for aromaticity in the two states (4n + 2 vs. 4n, respectively). The results show that substituents indeed influence the polarity of fulvenes in the two states, however, cooperative interactions between the substituents and the fulvene moiety are most pronounced in the ground state.     

Characterization of the singlet and triplet excited states of 3-chloro-4-methylumbelliferone

An extensive photophysical characterization of 3-chloro-4-methylumbelliferone (3Cl4MU) in the ground-state, S(0), first excited singlet state, S(1), and lowest triplet state, T(1), was undertaken in water, neutral ethanol, acidified ethanol, and basified ethanol. Quantitative measurements of quantum yields (fluorescence, phosphorescence, intersystem crossing, internal conversion, and singlet oxygen formation) together with lifetimes were obtained at room and low temperature in water, dioxane/water mixtures, and alcohols. The different transient species were assigned and a general kinetic scheme is presented, summarizing the excited-state multiequilibria of 3Cl4MU. In water, the equilibrium is restricted to neutral (N*) and anionic (A*) species, both in the ground (pK(a) = 7.2) and first excited singlet states (pK(a)* = 0.5). In dioxane/water mixtures (pH ca. 6), substantial changes of the kinetics of the S(1) state were observed with the appearance of an additional tautomeric T* species. In low water content mixtures (mixture 9:1 v:v), only the neutral (N*) and tautomeric (T*) forms of 3Cl4MU are observed, whereas at higher water content mixtures (water mole fraction superior to 0.45), all three species N*, T*, and A* coexist in the excited state. In the triplet state, in the nonprotic and nonpolar solvent dioxane, the observed transient signals were assigned as the triplet-triplet transition of the neutral form, N*(T(1)) → N*(T(n)). In water, two transient species were observed and are assigned as the triplets of the neutral N*(T(1)) and the anionic form, A*(T(1)) (also obtained in basified ethanol). The phosphorescence spectra and decays of 3Cl4MU, in neutral, acidified, and basified solutions, demonstrate that only these two species N*(T(1)) and A*(T(1)) exist in the lowest lying triplet state, T(1). The radiative channel was found dominant for the deactivation of the anionic species, whereas with the neutral the S(1) ? S(0) internal conversion competes with fluorescence. For both N* and A* the intersystem crossing yield represents a minor deactivation channel for S(1).     

Energies of the lowest singlet S and triplet S states of helium by the local energy method

The least squares local energy method is applied to the helium atom in greater detail in a formulation which can easily be extended to more complicated atoms. The energies of the 1 ¹ S and 2³ S states are calculated to be – 2.9025 H and – 2.1753 H respectively. These values are in excellent agreement with the non-relativistic values of – 2.9037 H and – 2.1752 H calculated by Pekeris.

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Zusammenfassung Die Methode, die Varianz der lokalen Energie zu minimisieren, wird in einer leicht auf kompliziertere Atome zu erweiternden Form ausführlicher auf das Heliumatom angewandt. Die Energien des 1 ¹ S – und des 2 ³ S–Zustandes werden zu – 2,9025 bzw. – 2,1753 at. E. berechnet. Diese Werte stimmen ausgezeichnet mit den von Pekeris berechneten nichtrelativistischen Werten von – 2,9037 bzw. – 2,1752 at. E. überein.

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Résumé Le calcul de l'énergie locale par la méthode des moindres carrés est appliqué plus en détail à l'atome d'hélium, dans une forme qui s'étend aisément à des atomes plus compliqués. Les énergies des états 1 ¹ S et 2 ³ S se calculent à – 2,9025 et – 2,1753 u. a., respectivement. Ces valeurs sont en excellent accord avec les valeurs de – 2,9037 et – 2,1752 u. a. (sans relativité) calculées par Pekeris.

     

Intra- and intermolecular electronic relaxation of the second excited singlet and the lowest excited triplet states of 1,3-dimethyl-4-thiouracil in solution

Intramolecular processes of deactivation of 1,3-dimethyl-4-thiouracil (DMTU) from the second excited singlet (S2) (pi, pi*) and the lowest excited triplet (T1) (pi, pi*) states have been studied using perfluoro-1,3-dimethylcyclohexane (PFDMCH) as a solvent. The spectral and photophysical (PP) properties of DMTU in CCl4, hexane and water have also been described. For the first time, the fluorescence from S2 state DMTU has been observed. The picosecond lifetime of DMTU in the S2 state (tau(S2)) in PFDMCH has been proposed to be determined by a very fast intramolecular reversible process of hydrogen abstraction from the ortho methyl group by the thiocarbonyl group. The shortening of tau(S2) in CCl4 is interpreted to be caused by the intermolecular interactions between DMTU (S2) and the solvent. Results of the phosphorescence decay as a function of DMTU concentration were analyzed using the Stern-Volmer formalism, which enabled determination of the intrinsic lifetime of the T1 state (tau0(T1)) and rate constants of self-quenching (k(sq)). The lifetimes, tau0(T1), of DMTU in PFDMCH and CCl4 are much longer than the values hitherto obtained in more reactive solvents. The PP properties of DMTU both in the S2 and T1 states have been shown to be determined by the thiocarbonyl group.     

Combined CI-HY studies of atomic states. IV. The four lowest 1S and four lowest 1P states of He and the lowest 1S and 1P states of H−1

Combined CI -HY method calculations are reported for the ground and first three excited S states of He with an error on the order of 10^?7 a.u. within the same 120-term basis. For He ¹P, the four lowest states are obtained with an error ≤2 × 10^?6 a.u. within the same 102-term basis. H^?1 S and ¹P states are also treated by the same CI -HY technique. The utility of an spd Slater-type orbital, r, v = 0, 1 basis is investigated, with indications that it might be an excellent basis for states of first row atoms.     

Field shifts and lowest order QED corrections for the ground 1 1S and 2 3S states of the helium atoms

The bound state properties of the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe helium atoms are determined to very high accuracy from the results of direct numerical computations. To compute the bound state properties of these atoms the author applied his exponential variational expansion in relative/perimetric three-body coordinates. For the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe atoms the author also determined the lowest order QED corrections and the field component of isotopic shift (=field shift). For the 2 3S(L=0) state of the 3He atom the hyperfine structure splitting is evaluated. The considered properties of the ground 1 1S state and the lowest 2 3S state in the 3He and 4He atoms are of great interest in a number of applications.     

A study of interaction in the lowest singlet and triplet states of H2

The potential energy curves of the ground state and the first excited state of H₂ are examined in terms of the electronic force acting on each nucleus. The results reveal the detailed course of events that occur when two hydrogen atoms with parallel and antiparallel electron spins approach one another from a large internuclear separation.