Prediction Of Excitation Energies Research Articles

Assessment of the Van Voorhis-Scuseria exchange-correlation functional for predicting excitation energies using time-dependent density functional theory

We assess the performance of the Van Voorhis–Scuseria exchange–correlation functional (VSXC), a kinetic-energy-density-dependent exchange–correlation functional recently developed in our group, for calculating vertical excitation energies using time-dependent density functional theory in a benchmark set of molecules. Overall, VSXC performs very well, with accuracy similar to that of hybrid functionals such as the hybrid Perdew–Burke–Ernzerhof functional and Becke's three parameter hybrid method with the Lee, Yang, and Parr correlation functional, which contain a portion of Hartree–Fock exchange.

Geometric derivatives of density functional theory excitation energies using gradient-corrected functionals

Density functional theory (DFT) is having increasing success in predicting excitation energies using the methods of time-dependent DFT. As a result, it should be possible to generate potential energy surfaces for excited states by adding the excitation energy, as a function of geometry, to the ground-state energy. It is easier to find stationary points such as minima and transition states if the gradient of the energy is known. The present Letter extends earlier work on the gradients on excited-state surfaces using SCF and LDA (local density approximation) methods, to use gradient-corrected and hybrid functionals. Some examples of geometry optimisations are given.

Accurate excitation energies from time-dependent density functional theory: Assessing the PBE0 model

We analyze the performance of a density functional model obtained by combining the Perdew–Burke–Erzenrhof (PBE) generalized gradient functional with a predetermined amount of exact exchange for predicting vertical electronic excitation energies within a time-dependent approach. Four molecules, namely, CO, H2CO, (CH3)2CO, and C2H4, have been chosen as benchmark cases. Our results show that this model (PBE0) provides accurate excitations both to valence and Rydberg states. Furthermore, the results are numerically close to those obtained using asymptotically correct exchange-correlation functionals. The performance of the PBE0 model for predicting excitation energies in larger molecules is assessed for benzene, pyridine, and naphthalene. Here, the PBE0 model provides results which are in fairly good agreement with experimental data and of similar quality to those obtained by more sophisticated (and time-consuming) post-Hartree–Fock methods.

Excitation energies of 1s 2 n d and 1s 2 n f states for the lithium isoelectronic sequence

The nonrelativistic energies of the 1s(2)nd and 1s(2)nf(n=6, 7, 8 and 9) states for the lithium isoelectronic sequence from Li I to Ne VIII are calculated by using a full core plus correlation method with multiconfiguration interaction wave function. Relativistic and mass-polarization effects on the energy are evaluated as the first-order perturbation theory. In most cases with nuclear charge, Z less than or equal to 7, the agreement between our predicted excitation energies and the experimental data is less than 1 cm(-1).

Application of density-functional theory to atomic resonances

Density-functional theory in the local-spin-density approximation has been applied to calculate the energy positions of low-lying resonance (autoionization) states of neutral atoms and positive ions. This method is very convenient for a quick, approximate prediction of excitation energies in collision experiments.

The excited electronic states of H2CSi

We have studied the excited electronic states of silylidene(1-silavinylidene), H2CSi, by ab initio quantum-mechanical methods to determine their equilibrium geometries, relative energies, and harmonic vibrational frequencies. Besides the ground A11 state, we have also studied the A21 and A23 states, obtained by exciting an electron from the π orbital of silylidene to a py lone pair orbital, and the B21 and B23 states obtained by exciting an electron from an a1 symmetry silicon lone pair orbital to the py orbital. We have also investigated the lowest-lying cation states. Our predictions of the geometries of the A11 ground state and second excited singlet state, B21, are in good agreement with the experimental results of Harper, Waddell, and Clouthier [J. Chem. Phys. 107, 8829 (1997)]. Our predicted excitation energies and excited state vibrational frequencies also agree well with experimental values. The geometry of the B̃ 1B2 state differs markedly, and unexpectedly, from that of the X̃ 1A1 and b̃ 3B2 states. We explain this as resulting from the large electron repulsion between the unpaired electrons in the B̃ state, which essentially reside on the same atom.

Neutron crystalline-electric-field spectroscopy of (R = Ce, Pr, Nd)

The ternary intermetallic compounds (R = light rare earth) crystallize in the hexagonal -type structure, like the heavy-fermion superconductor . In this paper we present powder neutron scattering and single-crystal magnetic susceptibility experiments on , which provide sufficient information for us to unambiguously determine the crystalline-electric-field (CEF) splitting of the multiplet of . The CEF parameters obtained for are extrapolated to those for and . For , the powder neutron scattering measurement of the two strongest CEF excitations confirms the reliability of the extrapolated CEF level diagram with an accuracy of better than 10% for the excitation energies. For , with a rather strong Kondo effect, the extrapolation yields a CEF level sequence similar to that derived from single-crystal susceptibility data, and the predicted excitation energy lies well inside the width of the broad inelastic magnetic peak observed by neutron scattering. The CEF parameters yield a magnetic anisotropy which is compatible with the magnetic structures observed in and , and predict no magnetic ordering for down to the lowest temperatures.

Isovector monopole excitation energies

Using a hydrodynamical model whose parameters have been adjusted to fit the polarizability and excitation energy of the giant dipole nuclear resonance we predict excitation energies of the isovector monopole resonance. The predicted values are in good agreement with experimental data. The mass dependence of the excitation energy is strongly influenced by nuclear geometry.

Spin-flip decomposition of the spectrum forZr90(p,n) atEp=160MeV

The transverse polarization transfer for the $^{90}\mathrm{Zr}$(p,n) reaction has been measured for ${E}_{\mathrm{p}=160}$ MeV and theta=0\ifmmode^\circ\else\textdegree\fi{}. A sequence of alternating unnatural parity and natural parity excitations is clearly revealed. Some of the observed features are consistent with the known or predicted excitation energies of \ensuremath{\Delta}L=0 and \ensuremath{\Delta}L=1 resonances.

The sub-Coulomb 12C + 12C resonances in a microscopic 12C+ 12C,α+ 20Ne, 8Be+ 16O cluster basis

The low- J resonances in the Coulomb barrier region of the 12 C+ 12C system are investigated in the framework of a microscopic cluster model basis including 12C+ 12C, α+ 20Ne, and su8 Be+ 16O fragment decompositions. Calculations are carried out in an orthogonality condition model approximation in which Pauli-forbidden components are properly excluded from the basis but in which the interaction among cluster fragments is approximated by a local potential, obtained from a gaussian NN interaction by a folding procedure leading to both spherical and Q · Q terms. Only minor adjustments of overall strength and fall-off parameters are introduced to gain a consistent picture of the low-energy spectrum in the separate rearrangement channels. The basis includes cluster relative motion excitations with oscillator quanta from 12 to 20 and is not quite rich enough to give a detailed quantitative comparison between theory and experiment. Predicted excitation energies are too high by ~ 3 MeV and predicted 12C partial widths are too small to indicate a well-developed surface-peaked molecular character; but it does appear possible to identify a 5 MeV region as the potential seat of the 0 +, 2 +, 4 + resonances. The number and approximate spacing of the resonance fine structure components are in agreement with experiment.

Cross sections and dynamical properties of a emitters produced in interactions of 12C at 86 MeV/n on medium and heavy targets

Cross sections, mean recoil ranges and angular distributions of radioactive a emitters produced in 12C, induced reactions at 1 GeV on medium and heavy targets are presented. A new on-line electrostatic collection device is used. A wide spectrum of heavy residues corresponding to various mass losses away from the target between D to 60 a.m.u. has been observed. A phenomenological analysis based on the statistical decay of possible precursors gives some information on the properties of the primary interaction. Losses of 10 to 30 nucleons can be partly fitted by the intranuclear cascade model. For greater mass losses, more collective primary interaction is needed. The abrasion-ablation model can produce such residues but in its clean cuts approximation the predicted excitation energy is too low.

Satellite structure in atomic spectra. I. Theoretical framework and application to excited states of the singly ionised rare gases

A model for the calculation of satellite structure in atomic spectra is presented. Based on numerical non-relativistic wavefunctions, it includes some of the effects of electron correlation via frozen-core CI calculations. The model is applied to the energies of the 2S, 2P0 and 2D states of the singly ionised rare gases Ne, Ar, Kr and Xe. The results agree with experiment to within 1 eV for most excitation energies in Ar, Kr and Xe, and for Ne when relaxation of the frozen core is accounted for. Some trends in excitation energies with atomic number are discussed, and the model's performance in the prediction of excitation energies is assessed.

Sulfur oxide: Low-lying bound molecular electronic states of SO

We present here the results of self-consistent field (SCF) and configuration interaction (CI) theoretical studies of seven low-lying electronic states of sulfur oxide. The basis set was of double zeta quality augmented with polarization functions. The CI space for each electronic state consisted of all configurations constructed from single and double substitutions of electrons from the valence orbitals of the Hartree–Fock reference occupation. Spectroscopic constants as well as dipole moments for each electronic state were predicted both at the SCF and CI levels of theory. Of particular significance is the prediction of excitation energies and properties for three low-lying states for which experimental information is either unavailable or only very recently available. These states are the c1Σ− state (Te=28 100±300 cm−1), the A′ 3Δ state (29 200±300 cm−1) and the A″ 3Σ+ state (30 200±300 cm−1).

Electron correlation effects on the excitation energies of the lowest triplet states of glyoxal

In an attempt to understand the ordering of excited states of glyoxal the 1Ag ground state and low-lying triplet states 3Au, 3Bu, and 3Bg have been studied with ab initio correlated wavefunctions. A double zeta basis set was used in the configuration interaction calculations, and ∼6000 Slater determinants were selected for each electronic state. The predicted CI adiabatic excitation energies Te are 21 800 cm−1 (3Au), 25 100 cm−1 (3Bu), and 29 300 cm−1 (3Bg). The effects of d functions and higher (than double) excitations (unlinked clusters) have also been evaluated. For the 3Bu state, both d functions and higher excitations raise the predicted Te value by perhaps as much as 5 000 cm−1. For the 3Bg state, d functions raise the predicted excitation energy but higher excitations have the opposite effect. It is concluded that the excitation energy of the 3Bu state is dramatically increased by correlation effects, while Te for the 3Au and 3Bg states is markedly decreased by correlation.

A search for alpha-particle vibrational states in 208Pb

The 204Hg( 16O, 12C) 208Pb reaction has been measured ( E i = 88 MeV, θ L = 80, 85, 90°) to search for 4p-4h “α-vibration” states in 208Pb. The expected strength is not observed near the predicted excitation energy.

Equations-of-motion method including renormalization and double-excitation mixing

The equations-of-motion method is discussed as an approach to calculating excitation energies and transition moments directly. The proposed solution [T. Shibuya and V. McKoy, Phys. Rev. A 2, 2208 (1970)] of these equations is extended in two ways. First we include the proper renormalization of the equations with respect to the ground state particle-hole densities. We then show how to include the effects of two-particle-hole components in excited states which are primarily single-particle-hole states. This is seen to be equivalent to a single-particle-hole theory with a normalized interaction. Applications to various diatomic and polyatomic molecules indicate that the theory can predict excitation energies and transition moments accurately and economically.

Configuration Mixing of Major Shells in Mass-16 and Mass-17 Nuclei

The odd-parity ($T=\frac{1}{2}$) levels of ${\mathrm{O}}^{17}$ are investigated within the framework of the spherical shell model in order to determine the importance of configuration mixing of the ($2s, 1d$) and $1p$ major shells. Particles in the $2{s}_{\frac{1}{2}}$ and $1{d}_{\frac{5}{2}}$ subshells and holes in the $1{p}_{\frac{1}{2}}$ subshell are considered. It is shown that a configuration space which includes both 2-particle-1-hole states and 4-particle-3-hole states is required to achieve good agreement between calculated and experimental energies in the range of excitation from 3.06 to 8.88 MeV. As confirmed by previous work, calculations based on a truncated 2-particle-1-hole space predict excitation energies that are higher by about 2 MeV than the observed values. In addition, the effects of $(2{s}_{\frac{1}{2}}, 1{d}_{\frac{5}{2}})\ensuremath{-}1{p}_{\frac{1}{2}}$ mixing on the odd- and even-parity ($T=1$) states of ${\mathrm{N}}^{16}$ above its four lowest levels are evaluated. The consequences of this mixing are a lowering of calculated energies by an average of 2-3 MeV and many changes in the predicted sequence of levels. The significance of these results in relation to the neutron elastic scattering cross section for ${\mathrm{N}}^{15}$ is discussed, and a need for more experimental data on the spins and parities of ${\mathrm{N}}^{16}$ levels is indicated.

On isobaric analogue states

The excitation energies of isobaric analogue states, i.e. the energetically lowest states with a given isobaric spin T, have been related to the symmetry and pairing energies of the respective nuclei. Symmetry parameters a(A) and pairing energies δ(A) were extracted from the experimental data. The parameter a(A) exhibits shell structure. An expression for the energetic difference between isobaric analogue states was established which reproduces the over 200 known values (known experimentally or calculated from the known masses of neighbouring isobars) up to A = 80 with a standard deviation of about 0.5 MeV. The same formula can be used to predict excitation energies of unknown isobaric analogue states and the masses of unknown neutron-rich and proton-rich nuclei. The above expression is in accordance with a theoretical expression based on an effective two-nucleon interaction. There exist small but systematic deviations from the supermultiplet model.