SCF and limited CI calculations for assignment of the Auger spectrum and of the satellites in the soft X-ray spectrum of H2O

SCF and limited CI calculations have been performed for a number of excited states of doubly ionized water. The calculations allowed an assignment of both the Auger spectrum and most of the satellites in the soft X-ray spectrum. The assignment for the two highest peaks in the Auger spectrum was ambiguous. SCF calculations of the K emission spectrum of H₂O were also performed. It was found that limited CI calculations were of importance for some states with two open shells in one symmetry. Such effects are caused by large off-diagonal lagrangian multiplies connecting the open shells in the reference configuration.     

SCF MO CI perturbation calculations of inner shell and valence shell vertical ionization potentials

A CI method for calculating inner and valence shell vertical ionization potentials is presented. It is based on ab initio SCF MO calculations for the neutral closedshell ground state followed by CI perturbation calculations for the ground and ion states including all spin and symmetry adapted singly and doubly excited configurations with respect to the main configurations of the state of interest. The state energy is computed by performing a CI calculation for a set of selected configurations, and then adding the contributions of the remaining configurations as estimated by second order Brillouin-Wigner perturbation theory. The use of the same set of MO's for all states together with the CI perturbation method makes the method rather rapid. The numerical results are, in spite of the limited Gaussian basis sets used, in good agreement with experiment.     

Role of the low-lying two-electron excited Ag states of C60 in contributing to its hyperpolarizability γ

The role of the low-lying two-electron excited ¹A_g states of C₆₀ in contributing to its hyperpolarizability γ is investigated by singly and doubly excited CI calculations in the semi-empirical CNDO/S approximation. It is found that inclusion of the doubly excited configurations is essential in evaluating γ. The calculated values of γ_zzzz(−3ω; ω, ω, ω) at wavelengths of ∞, 1.9, 1.83 μm sufficiently far from the first resonance are in reasonable agreement with experiment.     

Azulene: polarized absorption in stretched polymers and magnetic circular dichroism

Linear dichroic and magnetic circular dichroic spectroscopy is used to characterize the excited states of azulene. Comparison with crystal spectra underlines the necessity of using two-parameter equations for evaluations of stretched sheet spectra despite some previous claims to the contrary. The MCD spectrum reveals strong vibronic interactions in the second transition.The results are interpreted on the basis of Pariser—Parr—Pople (PPP) type calculations including some with extensive configuration interaction (CI). Calculated signs of the first three B terms spectrum agree with experimental signs irrespective of the details of the PPP model, and even the numerical values are in an order-of-magnitude agreement. Only the calculation with extensive CI gives agreement for signs of higher B terms. It suggest the possible presence of two excited states, but the present experimental evidence for these is insufficient. One of these new states would be best described as a predominantly doubly excited state.The origin of the B terms is traced to contributions due to magnetic mixing of individual zero-order excited states and the results permit determination of the absolute sense of magnetic dipole transition moments between excited states with respect to the sense of the vector product of the electronic dipole transition moments from the ground state to these excited states. A comparison is performed with B terms calculated using finite perturbation technique and gauge-invariant orbitals.     

Theory of single and double ionization of helium through two-photon excitation of the1 S 0 e (1) doubly excited resonance

We present a theory and calculations of two-photon-resonant three-photon ionization of He via the lowest even parity doubly excited state¹ S ₀ ^e (1). We assess the importance of double ionization relative to single ionization into excited ionic states. Although double ionization is found to be quite small in the present context, our calculations reveal the importance of autoionizing doubly excited states as virtual intermediate states and suggest contexts in which double ionization may be relatively more efficient.     

An AB initio SCF MO CI study of the n → π* transition of methylenimine

The electron correlation energies of both the ground and n → π* excited states of methylenimine (CH₂NH) are investigated by means of ab initio SCF MO CI calculations. Then n → π* singlet and triplet state energies of methylenimine are obtained through 3461-dimensional CI including the singly, doubly and triply excited configurations. the excitation energy from the ground state to the ¹(n → π*) state nearly coincides with that obtained in the framework of the singly excited configuration interaction (SECI) procedure. This result suggests that there is good cancellation of the correlation energy between the ground and the excited singlet sates, proving the usefulness of the SECI method for the excitation energies.     

Excited states of the benzyl radical

The CI method is used in the -electron approximation with orbitals for closed and open shells to calculate the properties of excited doublet states with allowance for all singly excited configurations and some doubly excited ones, and also for the first quartet and sextet states, which are calculated in the one-configuration approximation via the open-shell theory. The energies and transition moments agree satisfactorily with the available experimental evidence. A classification and assignment is given for the excited terms. Truncation of the complete set of singly excited configurations greatly distorts the calculated spectrum. Inclusion of doubly excited configurations in the CI also produces a substantial change in the spectrum; in some cases it alters the order of adjacent terms. Conversion in CI from basis closed-shell orbitals to open-shell ones produces a considerable lowering of all terms in the spectrum. As in the case of triplet terms for molecules, weakening of electron interaction brings the lowest excited term of the radical closer to the ground-state term. The electron-density and spin-density distributions are calculated for the excited states.     

Bound states of the barium atom by the hyperspherical approach

We present a nonadiabatic hyperspherical calculation of the highly excited and low lying doubly excited states of the barium atom using effective potentials for the two optically active electrons' interactions. Within the hyperspherical adiabatic approach the investigation of the spectra is performed with potential curves and nonadiabatic couplings of a unique radial variable, which allows clear identification of the states. The convergence of energy is obtained within well established bound limits, and the precision is comparable to accurate configuration interaction calculations. A very good agreement with experimental results is obtained with only few nonadiabatic couplings.     

The configuration interaction method,and the triplet-singlet splitting in CH2

A configuration-interaction (CI) method in which the interaction matrix is never constructed has been investigated, following the original suggestion of Roos. Two methods have been used (1) for singlet states, which can be represented by a one determinant configuration of doubly occupied orbitals, CI with all singly and doubly excited configurations, (2) for states for which the restricted self-consistent field approximation is a single determinant, CI with all singly and doubly excited determinants. In case (2), the wavefunction may not be exactly an eigenfunction of S ². The methods were investigated using a double-zeta plus polarisation basis for CH₂. Both methods must give the same result for the lowest singlet ground state. Keeping the bond length fixed at 2.10 and 2.04 bohr respectively the bond angle for the singlet and triplet were found to be 100.8 ° and 132.0 °, with energies ?39.0312 a.u. and ?39.0563 a.u. respectively. These are the lowest variational energies obtained for these systems; the singlet-triplet splitting is thus predicted to be 15.4 kcal/mol.     

On the nature of excited electronic states in cyanine dyes: implications for visual pigment spectra

CNDO/S CI calculations are carried out on polyenes and on cyanine dyes. In contrast to polyenes, doubly excited configurations have a strong effect on the first optically allowed excited state in cyanines. Protonated Schiff bases of retinal are closely related to cyanine dyes, with important consequences for models of visual pigment spectra and photochemistry.     

A size extensive energy functional derived from a double configuration interaction approach: the role of N representability conditions

Starting from a configuration interaction (CI) approach including only doubly excited configurations, the corresponding energy functional is modified by introduction of a topological factor in the normalization condition of the CI coefficients in such a way that it gets inherently size extensive. Constraints imposed by N representability conditions on the modified functional are discussed and lead to a specific choice of the topological factor. The basic variable in the modified energy functional is the second-order reduced density matrix parametrized in terms of CI-like coefficients. Test calculations for a variety of small molecules show that the numerical results obtained with the new functional are in very good agreement with those obtained from coupled cluster singles doubles calculations.     

On the calculations of the variational correlation energy using Møller—Plesset first-order wavefunctions

A method is developed, based on first-order symmetry-adapted pair functions obtained within the framework of the Rayleigh—Schrödinger Hartree—Fock perturbation theory, for obtaining a variational upper bound to the correlation energy in the form of pair increments. The correlation-energy functional obtained is written in terms of second- and third-order energy increments of Møller—Plesset perturbation theory. Application of the procedure to the ground states of the Ne-like systems yields energies of greater accuracy than those obtained from CI calculations using very extensive sets of singly and doubly excited configurations. Our pair energies and the total correlation energy obtained for Zn²⁺ represent the most accurate variational results reported so far for atomic systems containing 3d-electrons.     

An ab initio study of the ground and excited states of p-benzoquinone

The results of anab initio SCF calculation for the ground state and CI calculations for the excited states of p-benzoquinone are presented and discussed. A minimum basis set of Slater type orbitals was employed and the CI calculations were performed by considering single excitations from valence to virtual SCF molecular orbitals. The convergence of the calculated excitation energies is studied as a function of the number of orbitals used in the CI calculations. These calculations explain quite well the experimental results.     

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.     

Adiabatic hyperspherical study of three-particle systems

In an effort to unravel the dependence of the dynamics of three-particle systems on the relative mass of the particles, an adiabatic treatment in hyperspherical coordinates is used to study the ground state and some doubly excited states of several three-particle systems. Surprisingly, the binding energy of the ground state and of several doubly excited states exhibits a nearly linear dependence on the atomic reduced mass.     

Doubly-excited states for the Na2 molecule: application to the dynamics of the associative ionization reaction

In a recent paper, we have performed accurate model potential calculations for the adiabatic excited states of the Na₂ molecule. In view of dynamical calculations we propose a method to extract doubly excited potential curves, singly excited Rydberg series, and electronic couplings. In contrast to the previous work, the diabatic curves are correctly matching the adiabatic curves at large internuclear distances, and the electronic interactions do vanish in the asymptotic region. The adequacy of scaling laws to extract reduced parameters relevant to MQDT treatment of molecular autoionization is discussed. These parameters are used to calculate cross-sections for the associative ionization reaction at thermal collision energies when fine structure splitting can be neglected. In the framework of a simple model for the treatment of the long range dynamical couplings, we show the strong influence of the initial preparation of the atoms, and of long range population transfers. In contrast to the usual interpretation of experimental data, we predict that at least four doubly excited states may contribute efficiently to the process. Nevertheless, we may reproduce the marked variation of the observed ion signal as a function of the polarization of the exciting light. This work is a step towards a full treatment of the associative ionization between two cold atoms.     

Ab initio calculations of the excited states of the permanganate and chromate ions

The excited states of the permanganate and chromate ions are described by better-than-minimal basis set SC FMO CI calculations. The results are compared with the experimental absorption spectra.     

Cluster expansion of the wave function. Electron correlations in singlet and triplet excited states,ionized states,and electron attached states by SAC and SAC–CI theories

The symmetry-adapted-cluster (SAC ) and SAC –CI theories reported previously have been applied to the study of electron correlations in ground state, singlet and triplet excited states, ionized state, and electron attached state. Formulas for calculations of one-electron properties and transition properties from the SAC and SAC –CI wave functions are given. Calculations were carried out for the ground and Rydberg excited states of water and its positive and negative ions, with the use of the simpler computational scheme than the previous one. The results compare well with experiments.     

INDO-SCF and CI calculations on the trans-cis isomerization of azomethane in the ground state and in excited states

INDO-SCF calculations followed by CI calculations with inclusion of multiply, excited configurations were carried out to obtain potential energy curves for isomerization in the ground state and in some low-lying excited states of azomethane. The SCF wavefunctions are analyzed with the aid of newly defined bond characters providing a connection between the chemical concepts of bonds, lone-pairs, etc. and molecular orbital theory. Two different pathways for isomerization are considered and by comparison of the calculated results with experimental data it is concluded that this reaction proceeds in the ^1,3 (nπ*) states via rotation of both methyl groups around the NN double bond.     

Limited GSMO CI and ESMO CI study of electronic transitions in FNO

Limited CI calculations of vertical excitation energies and oscillator strengths have been performed in the ground state molecular orbital basis set (GSMO) and the excited state ones (ESMO). The absorption and emission spectrum of FNO is rediscussed on the basis of these calculations. The relaxation energy of excited states and the convergence of the CI expansion in the GSMO and ESMO basis sets is discussed.