Delocalized and localized pictures of excited and ionized states

The valence shell repolarization under a core ionization in a diatomic molecule as N₂ is analyzed through localized and delocalized pictures, showing their total equivalence. The interpretation is easier in the localized model, appearing mainly through local single excitation processes; in the delocalized model the repolarization effect is hidden (partly or totally) under double excitation processes involving simultaneous excitations in the valence shell and hole change in the core level, appearing therefore as a “correlation effect”. This effect is analyzed forn Be atoms, showing an ^?1 behaviour of the single excitations effect in the delocalized model, and explains the Hartree-Fock unstability numerically verified on O ₂ ⁺ , but it prevents to give any physical meaning to the “localization of the core hole in a diatomic molecule”.     

Influence of σ systems on the ππ* transition energies: A simple application to the series of linear polyenes

One uses a 2nd order perturbation expression of the transition energies for the series of linear polyenes with π delocalized molecular orbitals and σ fully localized bond molecular orbitals. One only keeps the σπ coulombic integrals and the local σσ ^* excitations. Within these assumptions it is possible to demonstrate: the effect of the monoexcitations on CH and CC bonds mainly depends of the pairing or non pairing character of the considered ππ ^* transition. It tends to zero as n ^?1 as the dimension n of the system increases. the rÔle of the \(\begin{array}{*{20}c} \sigma \\ \pi \\ \end{array} \left| {\begin{array}{*{20}c} {\sigma *} \\ {\pi *} \\ \end{array} } \right.\) excitations increases as n increases and tends towards a limit which depends of the considered ππ ^* transition. But the asymptotic final effect of σ system is smaller than for ethylene. the contribution of the σ system to the actual ππ ^* singlet triplet separation decreases towards zero when the dimension of the system increases.     

A Study of Excitation Delocalization/Localization in Multibranched Chromophores by Using Fluorescence Excitation Anisotropy Spectroscopy

We describe a simple approach to study the excitation localization/delocalization in multibranched chromophores by using fluorescence excitation anisotropy spectroscopy at room temperature. As examples, the electronic excitations in three different multibranched chromophores (dimers) are investigated. For a weakly coupled dimer, fluorescence anisotropy is independent of excitation wavelength, due to localized excitation as well as the degenerate electronic excited states. In contrast, in the case of a strongly coupled dimer, owing to excitonic splitting, a redistribution of the excitation energy is demonstrated by the dependence of anisotropy spectra on the excitation wavelength, which leads to significant deviation from the anisotropy signal of localized excitation. In particular, based on the law of additivity for anisotropy, the degree of delocalized excitation can be simply estimated for a given dimer.     

Application of the MC SCF method to the π → π* excitation energies of ethylene

The MC SCF method is employed to calculate the N → T and N → V π → π^* vertical excitation energies of ethylene. To obtain accurate excitation energies it is found to be necessary to utilize an expanded valence space containing two π and two π^* orbitals. Relatively small MC SCF calculations, allowing at most one-electron excitations from the sigma space, are found to yield excitation energies and spatial extents of the excited states in excellent agreement with the predictions of large multi-reference or iterative-natural-orbital CI calculations. These results show that within an MC SCF framework σ-σ correlation is unimportant for describing the π → π^* processes. We also conclude that the neglect of the effects of unlinked cluster terms in some of the CI calculations may have introduced small, but important, errors in the excitation energies and predictions of the spatial extent of the V state.     

Evaluating First-Order Molecular Properties of Delocalized Ionic or Excited States in Molecular Aggregates by Renormalized Excitonic Method

In the past few years, the renormalized excitonic model (REM) approach was developed as an efficient low-scaling ab initio excited state method, which assumes the low-lying excited states of the whole system are a linear combination of various single monomer excitations and utilizes the effective Hamiltonian theory to derive their couplings. In this work, we further extend the REM calculations for the evaluations of first-order molecular properties (e.g. charge population and transition dipole moment) of delocalized ionic or excited states in molecular aggregates, through generalizing the effective Hamiltonian theory to effective operator representation. Results from the test calculations for four different kinds of one dimensional (1D) molecular aggregates (ammonia, formaldehyde, ethylene and pyrrole) indicate that our new scheme can efficiently describe not only the energies but also wavefunction properties of the low-lying delocalized electronic states in large systems.     

An attempt to approach the solutions of the N-electron CNDO hamiltonian for conformational studies of conjugated systems

While dealing with the same N-electron hamiltonian, the SCF approximation and the third order PCILO results completely disagree about the conformation of conjugated systems. An attempt is made, using the CIPSI algorithm, to approach the exact solution of the N-electron CNDO hamiltonian for the butadiene molecule starting from either a priori localized, SCF localized or SCF delocalized MO's. The partial CI's performed from SCF delocalized MO's give arbitrary results when increasing the number of doubly excited determinants and Pancir?'s recent results is fortuitous; on the contrary the results obtained from a priori and SCF localized MO's have better convergence and consistence; from our best calculations the final solution seems to be a rather flat potential curve, the stable minimum being the trans planar minimum, with a second gauche minimum for θ = 120-150° (ΔH ≈ 1 kcal/mole), separated by a weak barrier (ΔH ≈ 2 kcal/mole). The third order PCILO solution is in much better agreement with this estimate of the exact solution than the SCF one.     

Local pair natural orbitals for excited states

We explore how in response calculations for excitation energies with wavefunction based (e.g., coupled cluster) methods the number of double excitation amplitudes can be reduced by means of truncated pair natural orbital (PNO) expansions and localized occupied orbitals. Using the CIS(D) approximation as a test model, we find that the number of double excitation amplitudes can be reduced dramatically with minor impact on the accuracy if the excited state wavefunction is expanded in state-specific PNOs generated from an approximate first-order guess wavefunction. As for ground states, the PNO truncation error can also for excitation energies be controlled by a single threshold related to generalized natural occupation numbers. The best performance is found with occupied orbitals which are localized by the Pipek-Mezey localization. For a large test set of excited states we find with this localization that already a PNO threshold of 10(-8)-10(-7), corresponding to an average of only 40-80 PNOs per pair, is sufficient to keep the PNO truncation error for vertical excitation energies below 0.01 eV. This is a significantly more rapid convergence with the number doubles amplitudes than in domain-based local response approaches. We demonstrate that the number of significant excited state PNOs scales asymptotically linearly with the system size in the worst case of completely delocalized excitations and sub-linearly whenever the chromophore does not increase with the system size. Moreover, we observe that the flexibility of state-specific PNOs to adapt to the character of an excitation allows for an almost unbiased treatment of local, delocalized and charge transfer excited states.     

Ab initio study of organic mixed valency

A series of six radical cations of the type (D L D)⁺ was investigated at the ab initio unrestricted Hartree–Fock level. One localized and one delocalized conformation were systematically searched by full geometry optimization. At both nuclear arrangements, mostly found as being minima in the symmetry‐restrained Hartree–Fock framework, excitation energies were calculated through the expansion of the wave function on single electronic excitations of the Hartree–Fock fundamental determinant and at the unrestricted Hartree–Fock or at the multiconfigurational self consistent field levels. Few calculations were also performed by taking into account some part of the electronic correlation. Except for N,N,N′,N′‐tetramethyl p‐phenylenediamine, all the studied compounds are localized stable cations, at the symmetry‐restrained Hartree–Fock level. However, the reoptimization of their wave function changes this observation since only three of them seem to conserve a localized stable conformation. Most of the studied systems are characterized by one or two excited electronic states very close to the fundamental one and should thus present an unresolved broadened first absorption band in the near‐infrared region. These features are in agreement with the available experimental data. Strong Hartree–Fock instabilities are found for the delocalized structure and put in relation with the existence of the large nonadiabatic coupling in this conformational region. The solvent influence is discussed in the Onsager dipolar reaction field framework. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 552–573, 2000     

Local orbitals for the study of the π→π* excitation in polyenes

Localized orbitals have recently been employed in large ab initio calculations, but their use has generally been restricted to ground‐state problems. In this work, we analyze the molecular orbitals of the excited states, optimized with a recently proposed local procedure. This method produces local orbitals of the CAS–SCF type, which permits its application to the study of excited states. In particular, we focus on the π→π* triplet excited state in polyenes, calculated using a 2/2 CAS space which includes two electrons in one π and one π* orbitals. In small polyenes, these two singly occupied active orbitals are delocalized all along the molecule. The extent of the delocalization is analyzed by studying polyenes of increasing size. Different polyenes have been studied, going from C₁₄H₁₆ to the C₇₀H₇₂ polyene. The relation of the π→π* excitation with the cation and anion systems is also discussed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The low-lying excitation energies of polyenes investigated with a chain-length-dependent screened potential

The chain-length dependencies of 2Ag and 1Bu excitation energies as well as their unexpected inversion observed experimentally in trans-polyenes have so far been explained satisfactorily only in terms of configuration interactions within the standard Pariser–Parr–Pople (PPP ) parametrization scheme with at least double excitations involving prohibitively large computational labor for long polyenes. A simpler calculation allowing nonzero differential overlap and employing restricted (first-order) single-excitation configuration interaction with chain-length-dependent screened potential is shown to provide an adequate alternative for the studies of those basic spectroscopic features of polyene excited states. The screening factor is parametrized in accordance with the chain-length-dependent behavior of the electrical polarizabilities of polyenes derived within the standard PPP approximation scheme. © 1993 John Wiley & Sons, Inc.     

Potential energy curves for ground and excited states of NaLi from ab initio calculations with effective core polarization potentials

Sixteen low-lying electronic states of NaLi are investigated by SCF/valence Cl calculations including core polarization effects by means of an effective potential. Spectroscopic constants are obtained with estimated uncertainties of ΔR_e ? 0.01 Å, Δω_e ? 0.6 cm^?1 and ΔD_e ? 80 cm^?1. From a comparison of experimental and theoretical G(υ) values, we suggest a ground-state dissociation energy of 7093 ± 5 cm^?1. Using our rovibrational energies and recently measured excitation lines, we are able to improve the T_e values and dissociation energies of five excited states to an accuracv of ±8 cm^?1.     

Quantum chemical ab initio calculations for excited states of F IV

Quantum chemical ab initio calculations have been performed for the ground state and for several excited states of the F³⁺ ion (F IV). Three levels of accuracy have been used: Frozen-core SCF calculations (FRC-SCF) to determine orbital energies ε _nl and quantum defects δ _l for excited Rydberg orbitalsnl; frozen-core SCF followed by CI calculations (FRC-CI) which account for multiplet splittings and configuration mixings, and multi-configuration coupled-electron-pair approximation (MC-CEPA) calculations which include dynamic correlation effects. The accuracy of the calculated excitation energies is in the order of 5000 cm^?1 at the FRC-CI level and in the order of 500 cm^?1 at the MC-CEPA level. This latter error amounts to about 0.1% for excitation energies in the range of 400000 to 600000 cm^?1. The MC-CEPA calculations have been performed for 17 experimentally known states and for 14 experimentally unknown states, in particular for the configurations 2s2p ² (² D)3s, 2s 2p ²(² S)3s, 2s ² 2p 4p, and 2s ² 2p 5p.     

Complete density matrix of HeI 3p excited in fast grazing ion-surface collisions via “Hanle-effect”

He⁺-ions with energies ranging from 6 to 25 keV are grazingly scattered off a clean and flat Al(111)-surface. We investigate the excitation of HeI 3p via fluorescent light emitted in the HeI 2s ³ S?3p ^{3 3} P transition. By observation of the polarization of light in dependence on an external longitudinal magnetic field (“Hanle-effect”), we deduce the complete density matrix of HeI 3p excited by fast ion-surface scattering.     

Ab initio MRD–CI calculations on cubane (neutral,carbocation, carboanion) and dissociation of nitrocubanes based on localized orbitals

Ab initio MRD –CI calculations based on localized orbitals were carried out for cubane (neutral, carbocation, carboanion) both in our customary MODPOT basis set and in an all-electron 4–31G basis set. The calculated MRD –CI charge distributions on C1 (the skeletal atom from which the H^? or H⁺ was removed) (ab initio MODPOT neutral 4.221, carbocation 3.796, carboanion 4.282; all-electron 4–31G neutral 6.171, carbocation 5.717, carboanion 6.078) indicate that the + or - charge does not remain localized on C1 but redistributes itself. This has significant implications for preparative reactions of energetically substituted cubanes. The MRD –CI population analyses differ somewhat from the SCF population analyses, especially in the calculated total overlap populations. To investigate this effect on electrostatic molecular potential contour (EMPC ) maps generated from SCF or MRD –CI wave functions, we wrote additional routines to calculate EMPC maps from MRD –CI wave functions. The EMPC maps generated from SCF or MRD –CI wave functions are different if the molecule needs an MRD –CI multideterminant wave function to describe it adequately. The EMPC map is a one-electron property. One-electron properties are derived from the 1-matrix. The 1-matrix is different for SCF or MRD –CI wave functions. Thus, all the one-electron properties (EMPC maps, population analyses, bond deviation indices, etc.) are different when calculated from SCF or MRD –CI wave functions if MRD –CI wave functions are necessary to describe a system properly. We calculate these one-electron properties from the 1-matrix from the final natural orbitals. Our preliminary calculations for the dissociation pathway indicate it takes more energy to dissociate a bond in 1-nitrocubane than in octanitrocubane. Even in their ground electronic states at equilibrium geometry, both 1-nitrocubane and octanitrocubane require MRD –CI wave functions to describe them properly. The c² of the single determinant SCF wave function is only 0.8401 for 1-nitrocubane and 0.8300 for octanitrocubane. There are contributions from skeletal excitations as there are for cubane itself as well as excitations involving the nitrogroup. As the bond in nitrocubane is dissociated to 8.00 bohrs, the c² of the SCF contribution drops to only 0.4606 (1-nitrocubane) and 0.4445 (octanitrocubane). At this C₁? N₁ intermolecular distance, the largest excitations are in the C₁? N₁ bond: (C₁? N₁)² → (C₁? N₁*)², (C₁? N₁) → (C₁? N₁*). We also calculated the first electronically excited state for the dissociation pathway for selected points for both 1-nitrocubane and octanitrocubane.     

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.     

Spectroscopy of photovoltaic and photoconductive nanocrystalline Co2+-doped ZnO electrodes

Photocurrent and photoconductivity measurements have been used in combination with absorption and magnetic circular dichroism (MCD) spectroscopic measurements to elucidate the mechanism of photoinduced carrier generation in nanocrystalline Co(2+):ZnO electrodes. These experiments allowed direct observation of two broad Co(2+) charge transfer (CT) bands extending throughout the visible energy range. The lower energy CT transition is assigned as a Co(2+) --> conduction band excitation (ML(CB)CT). Sensitization of this ML(CB)CT level by (4)A(2) --> (4)T(1)(P) ligand-field excitation is concluded to be responsible for the distinctive structured photocurrent action spectrum of these electrodes at ca. 14 000 cm(-1). The higher energy CT transition is assigned as a valence band --> Co(2+) excitation (L(VB)MCT) and is found to have an internal quantum efficiency for charge separation that is approximately four times larger than that of the ML(CB)CT excitation. The different internal quantum efficiencies for the two CT excitations are related to differences in excited-state wave functions arising from configuration interaction with the 1S excitonic levels of ZnO. Whereas the ML(CB)CT excited state is best described as a localized Co(3+) + e(-)(CB) configuration, the L(VB)MCT excited state (Co(+) + h(+)(VB)) has a 4-fold greater admixture of delocalized excitonic (Co(2+) + h(+)(VB) + e(-)(CB)) character in its wave function, a conclusion supported by quantitative analysis of the CT absorption intensities. Practical factors controlling the overall photovoltaic efficiencies of the photoelectrochemical cells, including electrode conductivity and porosity, were also examined.