The Hartree-Fock method with orthogonality restrictions for doubly excited and ionized states

It is shown that the doubly excited and ionized states with vacancies in the K electronic shells can be considered within the framework of the same scheme on the basis of the asymptotic projection method proposed earlier. In contrast to the conventional methods, the electron detachment effect is achieved by imposing the requirement that the orbitals of the excited (hole) state be orthogonal to the orbitals of removed electrons. The solution of equations that determine the orbitals is implemented in terms of the conventional spin-unrestricted Hartree-Fock method with additional conditions that ensure the spin purity and provide a unique choice of the zero-order approximation in constructing the many-particle perturbation theory for taking into account the correlation effects. The performance of the method is demonstrated by calculating the excitation energies and ionization potentials corresponding to the removal of electrons from the inner K-shell.     

Identification of excited singlet states of chlorophenol isomers

The UV spectra of optical absorption of para-, meta-, and ortho-chlorophenol are recorded in the gas phase. The bands of UV spectra are assigned to the electronic transitions of molecules to definite excited singlet states on the basis of calculations by the TDDFT B3LYP/6-311++G(d, p) method. In each case the electron configuration making the predominant contribution to the particular singlet state is determined. The energies of singlet electronic transitions are shown to depend on the energy spacing between the molecular orbitals involved in these transitions.     

The lowest singlet and triplet excited states of pyrazine

The phosphoresence, fluorescence and absorption spectra of pyrazine-h₄ and -d₄ have been obtained at 4°K in a benzene matrix. For comparison, those of the isotopically mixed crystal pyrazine-h₄ in d₄ were also taken. All these spectra show extremely sharp and well-resolved lines and reveal detailed vibronic structure.The coincidence of origins of absorption and emission shows that the lowest singlet state is an allowed transition, properly designated as ${}^1\text{B}{}_{\mathrm{3u}}\text{←}{}^1\text{A}{}_{\mathrm{1g}}$. The forbidden component ¹B_2g, predicted by both “exciton” and MO theories to be below the allowed component, must lie higher. Its exact location still remains uncertain.The phosphorescence spectrum, when compared with the singlet-triplet excitation spectrum, indicates that the lowest triplet state is also symmetry allowed, showing a strong 0-0 band and the coincidence of origins of absorption and emission. In accordance with previous work, the triplet state is designated as ³B_3u.The vibronic structure of the phosphorescence spectrum is very complicated. The first work on the analysis of this spectrum concluded that a simple progression of ν_6a exists. Under the high resolution attainable in the present experiments, the supposed ν_6a progression proves to have a composite structure, starting from the second member of the progression. Not only is the ν_9a hydrogen-bending mode present as shown by the appearance of the CD bending mode in the d₄ spectrum, but a band assigned as 2ν_6b was also identified. The latter's anomalous intensity in the phosphorescence spectrum is interpreted as due to the Fermi resonance with 2ν_6a and ν_9a bands. To help resolve the present controversy over the origin of the phosphoresence spectrum observed in crystalline pyrazine, detailed vibrational analyses of the emission spectra were made. The fluorescence spectrum has essentially the same vibronic structure as the phosphorescence spectrum.     

Identification of singlet excited electronic states of toluidine isomers

The photoelectron and UV absorption spectra of para-, meta-, and ortho-toluidine in the gas phase are obtained. The photoelectron spectra in the energy region up to 15.5 eV are interpreted based on the B3LYP/6-311+G(d, p) calculations. Based on the TDDFT B3LYP/6-311+G(d, p) calculations and taking into account the obtained interpretation of photoelectron spectra, the UV absorption bands are assigned to particular singlet transitions. For each transition, the electron configuration that makes the dominant contribution to the transition is determined. It is shown that the transition energy for toluidine isomers depends on the energy gap between the corresponding occupied and unoccupied molecular orbitals. It is noted that this dependence is similar for different benzene derivatives.     

Variational method for excited atomic states

An analysis is presented of the extremum properties of energy functionals for the excited states of many-electron systems, in particular, atoms, in the case when there exist low-lying states of the same symmetry as the excited state under consideration. Two theorems are proved concerning the relationship between the upper bound on the eigenvalues corresponding to the excited states and the extremum properties of the energy functional determined by variational test functions which depend on parameters. In this context, different variants of the one-electron approximation used in the excited-state calculations are considered: the method of obtaining self-consistent solutions with one-electron functions orthogonal within the configurations (the Hartree-Fock method for configurations); the frozen atomic core approximation for the excited configuration; the method of nonorthogonal orbitals in the excited configuration; and the approximation of the frozen ionic core. Cases are identified and reasons given for the possible collapse of the excited state energy level to an unjustifiably low value of the energy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 18–33, August, 1990.     

Identification of singlet excited electronic states of hydroxybenzoic acid isomers

The photoelectron spectra of benzoic and para-, meta-, and ortho-hydroxybenzoic acids and their UV absorption spectra in ethanol are obtained. The photoelectron spectra in the energy region up to 15.5 eV are interpreted based on the B3LYP/6-311+G(d, p) calculations. Based on the TDDFT B3LYP/6-311+G(d, p) calculations and taking into account the obtained interpretation of photoelectron spectra, the UV absorption bands are assigned to particular singlet transitions. For each transition, the electron configuration that makes the main contribution to the transition is determined. It is shown that the transition energy depends on the energy gap between the corresponding occupied and unoccupied molecular orbitals.     

Mixing of singlet and triplet exciton states in highly excited CdS

Fluorescence spectra due to the free excitons have been studied in CdS at 4.2 K under various excitation levels. It has been found that the triplet-exciton emission intensity relative to the singlet line is enhanced remarkably with the excitation power density. This effect is reasonably explained by the mixing of the singlet with the triplet through the many body interaction. The density of optically generated excitons is determined from the magnetic field dependence of the triplet emission intensity.     

Theoretical study of the electronic ground states and low-lying singlet excited states of thiophene-based spirofluorenes

The electronic structures and optical properties of oligothiophene substituted spirofluorenes are investigated theoretically with semi-empirical quantum chemical calculations. A theoretical investigation of the interaction between two perpendicular π-systems of various oligothiophene substituted spirofluorenes is conducted. The results demonstrate that the interaction between two perpendicular branches is reduced by oligothiophene substitutions. Photoexcitation induced relaxation is mainly located on one of...     

The out-of-plane vibrational modes of chlorobenzene in its ground and first singlet excited states

The study of 2699 Å electronic band system of chlorobenzene has been extended to extract out all the six b₁ and three a₂ modes in both the ground state (^eA₁) and the electronically excited first singlet state (^eB₂). The procedure of the extraction of these modes on the basis of observed sequences, cross-sequences, and overtones has especially been elaborated. Strong Fermi interaction has been observed between the vibrational level ν′_6b and combination level ν′_16a + ν′_16b in ^eB₂ state. The uniqueness of the assignments of the modes has been critically discussed.     

A new method for determining excited states of quantum systems

Summary A new method for computing excited states of a given operatorH is here presented. Our procedure is of particular value when its representation requires an orthonormal basis set of large dimension. In order to obtain the excited state ofH nearest in energy to any chosen trial energyE _t, we consider the auxiliary operatorA=(H−E _t)². We show that a reasonable number of relaxations on appropriately generated low-order Krylov subspaces forA is sufficient to produce better and better approximations of its ground state; a high-accuracy final refinement of the ground state ofA is then possible through the standard Lanczos procedure. An important feature of our method is that storage memory limitations, encountered in the conventional determination of all eigenvalues of large systems, are here overcome. As an illustration of the method two significant examples are discussed. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Hartree-Fock energies of D and D doubly excited states of the lithium isoelectronic sequence

Hartree-Fock energies of 1s2snd ⁴D, 1s2pnp ⁴D and 1s2pnd ⁴D⁰, n=3–5 of lithium isoelectronic sequence from Li to Ne⁺⁷ are reported. These results in conjunction with the energy of the lowest ⁴P and ⁴P⁰ states of the lithium isoelectronic sequence as calculated by Holoien and Geltman, are used to check some proposed assignments of lines obtained in beamfoil spectroscopy of Be(II), C(IV) and N(V).     

Positron and electron energy bands in several ionic crystals using restricted Hartree-Fock method

Using a restricted Hartree-Fock formalism and suitably localized and symmetrized wave functions, both the positron and electron energy bands were calculated for NaF, MgO and NiO. The lowest positron state at Γ₁ lies above the vacuum level and negative work functions are predicted. Positron annihilation rates were calculated and found to be in good agreement with measured lifetimes.     

Electronic transition moments between excited singlet states of the H2 molecule

The twelve transition moments which connect each of the three ¹Σ_g⁺ states EF, GK, and $\text{H}\text{H}$ with the three ¹Σ_u⁺ states B,B′, $\text{B″}\text{B}$ and with the state C¹Π_u were computed in the range of internuclear distances 1.25 ≤ R ≤ 15 a.u. using accurate electronic wavefunctions. The relative phases of the wavefunctions, which determine the signs of the transition moments, were consistently defined at all R values. The strong R dependences of the transition moments reflect the R-dependent changes in electronic character of the states involved in these transitions. At large R values the ¹Σ_g⁺-¹Σ_u⁺ transition moments are dominated by the two-electron charge resonance in the ionic configuration H⁺ + H^? whose transition moment is $\text{M(R) ? R}$.