Radial and angular correlations in doubly excited states: A time‐dependent perturbation approach

The time‐dependent variation perturbation theory (TDVPT) was applied to estimate separately the effect of radial and angular correlations in the doubly excited states of two‐electron systems. Test calculations were performed for the transitions 1s² : ¹S^e→2s² : ¹S^e for H⁻ and 1s² : ¹S^e→ns² : ¹S^e (n=2,…,5) for He, Li⁺, Be²⁺, and B³⁺. Transition energies to various doubly excited states were estimated using radially correlated basis sets as well as with basis sets which take care of both radial and angular correlations. Angular correlation is taken care of by incorporating higher angular momentum basis sets in the expansion of the perturbed wave functions. The excitation energy is lower in all the cases, indicating the correct behavior. Overall improvement of the results is observed when angular correlation is included. The effect of angular correlation, however, diminishes rapidly with increase of the nuclear charge. This has been demonstrated explicitly for the lowest doubly excited transitions in the highly stripped ions Al¹¹⁺, Si¹²⁺, P¹³⁺, S¹⁴⁺, and Cl¹⁵⁺. © 1999 John Wiley & Sons, Inc. Int J Quant Chem 76: 99–104, 2000     

Effect of Debye plasma on the doubly excited states of highly stripped ions

Pilot calculations have been performed to study the effect of surrounding plasma on several doubly excited states for a few astrophysically important, highly stripped ions of helium isoelectronic sequence Al¹¹⁺, Si¹²⁺, P¹³⁺, S¹⁴⁺, and Cl¹⁵⁺. The transitions from 1s²:¹S^e → 2s²:¹S^e, 2p²:¹D^e, 2s2p:¹P^o, 2s3d:¹D^e and 2p3d:¹F^o are studied. The effect of the plasma background is taken care of using the Debye screening model which admits of a wide variety of plasma conditions. Transition energies as well as the analytical wave functions of the doubly excited states have been obtained from a study of the pole positions of the collective oscillation modes in the two‐electron charge cloud under a time‐dependent harmonic perturbation. The response properties of the system are analyzed from the linearized version of a suitably constructed variational functional. Most of the calculated data are new. Our results agree well with the relatively few existing experimental and theoretical data for the free ions. The general trend of the results show systematic behavior with respect to increased plasma strength, and the data may be useful from the astrophysical viewpoint. The doubly excited state wave functions have been used to calculate the Coulomb repulsion integrals to check their consistency and may be useful for evaluating other physical properties connected with transitions and also estimating the rate coefficients for dielectronic recombination processes, which play a major role in the diagnostic determination of high‐temperature plasmas. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Self-consistent calculation of excited 3P state wave functions of atoms

A variation perturbation method in the Hartree–Fock scheme has been described to calculate excited ³P state wave functions of atoms. The starting wave functions are obtained from a study of the singularities in the dynamic polarizability calculation [1]. The 2³P, 3³P and 4³P states of He, Li⁺, Be²⁺, B³⁺ and C⁴⁺ are studied. The results obtained are in satisfactory agreement with experimental values and with other accurate theoretical estimates.     

Complex‐scaling calculations for resonance states of he with screened coulomb potentials

The doubly excited ¹S^e, ¹P^o, and ¹D^e resonance states of helium atom with screened Coulomb potentials are investigated. The complex scaling method with configuration interaction type basis functions are employed to extract the resonances associated with the He⁺(N = 2, 3, and 4) thresholds. 18 resonances (six below each of the He⁺ threshold) for each angular‐momentum state are calculated. The results lying below the He⁺(N = 2) threshold are in good agreement with previous calculations by the stabilization method with correlated basis wave functions. The ¹P^o and ¹D^e resonance states lying below the He⁺(N = 3 and 4) thresholds in the screening environment are reported for the first time. © 2013 Wiley Periodicals, Inc.     

Unnatural parity states of helium with screened Coulomb potentials

Effect of screened Coulomb (Yukawa) potentials on the doubly excited meta‐stable bound states and the resonance states with unnatural parities of the helium atom have been investigated in the framework of stabilization method using CI‐type basis functions. A total of 54 resonances (6 each of ¹D^o and ³D^o states, 12 each of ¹F^e and ³F^e states, 9 each of ¹G^o and ³G^o states) below the He⁺(3P) thresholds have been estimated by calculating the density of resonance states using a stabilization method. The resonances belong to the different 3lnl′ (n ≥ 3) series. We have also calculated the doubly excited ^1,3F^e and ^1,3G^o meta‐stable bound states of He atom below the He⁺ (2P) thresholds. The resonance energies and widths along with the meta‐stable bound states energies are reported for various screening parameters. In free atom case, some of the F‐wave resonance states and most of the cases, F‐ and G‐wave resonance widths are reported for the first time. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Doubly excited states of highly stripped ions: a time dependent perturbation approach

Doubly excited singlet states have been calculated for the astrophysically important highly stripped He like ions Al^{11 +}, Si^{12 +}, P^{13 +}, S^{14 +} and Cl^{15 +} for the transitions 2s ²: ¹ S ^e, 2p ²: ¹ D ^e, 2snp: ¹ P ⁰, 2snd: ¹ D ^e and 2pnd: ¹F⁰ for n45. The transition energies are obtained from the position of resonances in the oscillations of the two electron charge cloud under an external harmonic perturbation. Linearised version of a suitably constructed variational functional is used for obtaining the response properties of the system. Most of the results are new. Agreement with the only few existing experimental data along this line is very reasonable. Analytic representations of the doubly excited states are obtained and the Coulomb repulsion integral in these states are estimated for checking the consistency of the wavefunctions. The doubly excited state wavefunctions so obtained may be used for evaluating other physical properties connected with transitions.     

Resonances in helium atoms associated with theN=4 andN=5 He+ thresholds

Some doubly excited autoionising states of helium atoms converging on theN=4 andN=5 He⁺ thresholds are calculated by use of a method of complex-coordinates. States withL≧2 and with parities of (?1) ^L and (?1) ^L+1 are calculated by using products of Slater-orbital type wave functions with expansion lengths up to 319 terms. Resonance parameters (both resonance energy and autoinoisation width) are calculated for states with angular momentum up toL=7 forN=4 resonances, andL=8 forN=5 resonances.     

Self-consistent calculation of excited 1P state wave functions of atoms

In an earlier paper (Bibliography [1]) it has been shown that approximate representations of excited states of atoms can be obtained from the study of the singularities in the dynamic polarizability. Starting with these wave functions a more accurate calculation of the excited states in the Hartree–Fock scheme can be made by a perturbation treatment. The resulting wave functions yield significantly improved energy values. The 2¹P, 3¹P and 4¹P states of the He sequence up to C⁴⁺ are studied. The expectation values of a number of operators are calculated. The results obtained by the present method compare favourably with other elaborate calculations.     

Calculations of D‐wave bound states and resonance states of the screened helium atom using correlated exponential wave functions

We have investigated the effects of screened Coulomb (Yukawa) potentials on the bound ^1,3D states and the doubly excited ^1,3 D^e resonance states of helium atom using highly correlated exponential basis functions. The Density of resonance states are calculated using stabilization method. Highly correlated exponential basis functions are used to consider the correlation effect between the charged particles. A total of 18 resonances (nine each for ¹ D^e and ³ D^e states) below the n = 2 He ⁺ threshold has been calculated. For each spin states, this includes four members in the 2pnp series, three members in the 2snd series, and two members in 2pnf series. The resonance energies and widths for various screening parameters ranging from infinity to a small value for these ^1,3 D^e resonance states are reported along with the bound‐excited 1s3d ^1,3 D state energies. Overall behavior of the spectral profile of 1s3d ¹D state of helium atom due to electron‐electron and electron‐nucleus screening are also presented. Accurate resonance energies and widths are also reported for He in vacuum. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

On Excited States of Alkyl Bridged [14] Annulenes

The linear dichroic absorption spectrum of 1,3,6,8-trans-15, 16-hexamethyl-dihydropyrene has been measured in stretched polyethylene at 77K, and CNDO-CI calculations with inclusion of singly and doubly excited configurations have been carried out on a series of alkyl bridged [14] annulenes with pyrene- and anthracene-shaped perimeters. Transitions to e_3g → e_4u type ¹B states are well described, and the results indicate that additional low-energy excited states originate from e_3g→ e_5g and e_2u → e_4u type configurations interacting strongly with doubly excited configurations of the e_3g, e_3g → e_4u, e_4u type. The second excited singlet state responsible for the weak transition observed between the ¹L bands may be assigned to one of these additional states, but it is probably of complex nature, similar to the ‘phantom’ state in linear polyenes.     

Spectroscopic properties and potential energy curves of some low-lying electronic states of AlO,AlO+, LaO,and LaO+: An ab initio CASSCF study

Results of CASSCF state-averaged calculations on the lowest electronic states of LaO and LaO⁺ are reported in this work. For comparison, some low-lying electronic states of AlO and AlO⁺ are also reported. The ground state of LaO was found to be the X²Σ⁺ (R_e = 1.987 Å, ω_e = 794 cm^?1) with a low-lying A²Δ excited state. Five more excited states below 26000 cm^?1 were found. The first ionization potential (IP ) is found at 5.16 eV, resulting in an X¹Σ⁺ ground state for the LaO⁺ diatom, in opposition to AlO⁺ for which an X³ Π ground state has been found. Analysis of the wave functions, dipole moments, and Mulliken populations reveal that the bonding is quite ionic in both systems. © 1994 John Wiley & Sons, Inc.     

Ab initio spectroscopic study for the NaRb molecule in ground and excited states

A wide adiabatic study is performed for NaRb molecule, involving 15¹Σ⁺ electronic states including the ionic state Na^?Rb⁺, as well as 14³Σ⁺, 1–9^1,3Π, and 1–5^1,3Δ states. This investigation is performed using an ab initio approach which involves the effective core potential, the core polarization potential with l‐dependent cut‐off functions. The NaRb system has been treated as a two‐electron system and the full valence configuration interaction is easily achieved. The spectroscopic constants R_e, D_e, T_e, ω_e, ω_ex_e, B_e, and D₀ for all these states are derived. We have also computed the vibrational levels as well their spacing for different values of J. In addition, permanent and transition dipole moments are determined and analyzed. The Dunham coefficients have been used to perform experimental spacing to compare directly with our results. The present calculations on NaRb extend previous theoretical works to numerous electronic excited states in the various symmetries. © 2014 Wiley Periodicals, Inc.     

Ab initio calculations for the potential curves and spin–orbit coupling of Mg2

 The ground state and several low-lying excited states of the Mg₂ dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A¹Σ _u ⁺ excited state of Mg₂ is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants D _e, R _e and ω_e deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg₂ have been evaluated as a function of internuclear separation. Received: 10 May 2001 / Accepted: 15 August 2001 / Published online: 30 October 2001     

Ab initio interaction and spectral properties of CO+–He

In this contribution, ab initio methods have been used to study the open-shell CO⁺–He van der Waals (vdW) complex in both the ground and the first Π excited electronic state. Calculations were performed at the UCCSD(T) level of theory in the framework of the supermolecule approach using the cc-pVTZ basis set complemented with a set of standard bond functions in the middle of the vdW bond. Calculations predict a most-stable equilibrium conformation with β e=45°, R _e =2.85 Å and D _e =275 cm^?1 for the ground CO⁺(X²Σ)–He(¹S) state and β e=90°, R _e =2.70 Å and D _e =218 cm^?1 for the excited CO ⁺(A²Π)–He(¹S) state. The dipole moment μ and independent components of the field polarizability α of the CO ⁺–He vdW complex have been studied at the calculated equilibrium geometry of these states. The vertical excitation energies from the ground CO⁺(X ²Σ)–He(¹S) to the excited CO⁺(A²Π)–He (¹S) electronic state and corresponding shifts in the fluorescent spectrum with respect to the isolated CO⁺ molecule are also presented     

Spectral properties of helium‐like ions under strongly coupled plasma conditions

Systematic investigations have been performed to study the effect of strongly coupled plasma on the dynamic polarizabilities, low‐lying energy levels, oscillator strengths, and transition probabilities for the helium isoelectronic ions Li⁺, Be²⁺, B³⁺, C⁴⁺, N⁵⁺, O⁶⁺, F⁷⁺, and Ne⁸⁺. An ion‐sphere (IS) model of the plasma has been adopted and time‐dependent perturbation theory has been applied to calculate the energy levels and other transition properties. Systematic trend is observed for the spectroscopic properties along the isoelectronic sequence under a given plasma strength and also for a given ion under different plasma strengths. The ionization potential for a given ion is found to decrease, and the number of bound excited states has become finite under increased plasma strengths. The spectral line shifts under such plasma environment have been calculated. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Degenerate symmetry-adapted perturbation theory of weak interactions between closed- and open-shell monomers: application to Rydberg states of helium hydride

Symmetry-adapted perturbation theory is extended to the (quasi) degenerate, open-shell case. The new formalism is tested in calculations of the interaction energies for a helium atom in the ground state interacting with an excited hydrogen atom. It is shown that the method gives satisfactory results if the coupling with higher Rydberg states of the dimer is small, as is the case for the A²Σ⁺,B²Π,E²Π,3²Π, and 1²Δ states of HeH. For the C²Σ⁺ state convergence of the method is very slow, but it can be improved by including the n=3 states in the model space. Received: 3 June 1998 / Accepted: 9 September 1998 / Published online: 7 December 1998     

Expanded electronic states of the fluorine molecule

Potential curves of electronically excited states of F₂ with an expanded outer orbital have been calculated using a modified frozen core technique: The ionic core has been described with a two-determinant wave function and for the excited states a mixing of configurations with different cores has been employed. An investigation of the valence shell states of F₂ is presented and potential curves for a singly excited as well as a doubly excited V-state of ¹Σ_u⁺ symmetry have been calculated. Further a low lying two-configuration state resulting from simultaneous excitation to a valence and a Rydberg orbital is predicted.     

Theoretical study of the π→π* excited states of linear polyenes: The energy gap between 11Bu+ and 21Ag− states and their character

Multireference perturbation theory with complete active space self-consistent field (CASSCF) reference functions is applied to the study of the valence π→π* excited states of 1,3-butadiene, 1,3,5-hexatriene, 1,3,5,7-octatetraene, and 1,3,5,7,9-decapentaene. Our focus was put on determining the nature of the two lowest-lying singlet excited states, 1¹B_u⁺ and 2¹A_g⁻, and their ordering. The 1¹B_u⁺ state is a singly excited state with an ionic nature originating from the HOMO→LUMO one-electron transition while the covalent 2¹A_g⁻ state is the doubly excited state which comes mainly from the (HOMO)²→(LUMO)² transition. The active-space and basis-set effects are taken into account to estimate the excitation energies of larger polyenes. For butadiene, the 1¹B_u⁺ state is calculated to be slightly lower by 0.1 eV than the doubly excited 2¹A_g⁻ state at the ground-state equilibrium geometry. For hexatriene, our calculations predict the two states to be virtually degenerate. Octatetraene is the first polyene for which we predict that the 2¹A_g⁻ state is the lowest excited singlet state at the ground-state geometry. The present theory also indicates that the 2¹A_g⁻ state lies clearly below the 1¹B_u⁺ state in decapentaene with the energy gap of 0.4 eV. The 0–0 transition and the emission energies are also calculated using the planar C_2h relaxed excited-state geometries. The covalent 2¹A_g⁻ state is much more sensitive to the geometry variation than is the ionic 1¹B_u⁺ state, which places the 2¹A_g⁻ state significantly below the 1¹B_u⁺ state at the relaxed geometry. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 157–175, 1998     

Optical oscillator strengths for isoelectronic ions of nitrogen

An analytic atomic active electron model potential adjusted to experimental single-particle energy levels is used to generate wave functions for the valence and excited states of O¹⁺, F²⁺, Ne³⁺, Na⁴⁺, and Mg⁵⁺. Using these wave functions in conjunction with the Born approximation and the LS-coupling scheme, we calculate optical oscillator strengths for excitations from the 1s²2s²2p³(⁴S_3/2) ground state. The results are compared to experimental data and other calculations. Systematic trends along the isoelectronic sequence are discussed.