PCILO method for excited states

The zeroth order excitonic wave-function built previously is considered as a zeroth order wave-function for the excited state. The interaction with other singly, doubly and triply excited determinants is taken into account through a 2^nd order perturbation process. A proper definition of the unperturbed Hamiltonian allows cancellation between the ground state and excited state series, and thus the direct calculation of transition energies. The complete localization of MO's in the CNDO approximation makes the calculation very rapid. The method is applied to the series of linear polyenes H-(CH=CH) _N -H(2N7) with the CNDO/2 parametrization. The evolution of the excitonic wave-function is analyzed.

---

Zusammenfassung Die zuvor konstruierte excitonische Wellenfunktion nullter Ordnung wird als Wellenfunktion nullter Ordnung für den angeregten Zustand verwendet. Die Wechselwirkung mit anderen einfach, doppelt und dreifach angeregten Determinanten wird mittels Störungsrechnung 2. Ordnung berücksichtigt. Bei geeigneter Wahl des ungestörten Hamiltonoperators hebt sich der Grundzustand bei Berechnung der Übergangsenergien heraus, was auf ihre direkte Bestimmung hinausläuft. Die vollständige Lokalisierung der MO's hat zur Folge, daß bei Anwendung des CNDO-Verfahrens die Berechnung sehr schnell vonstatten geht. Die Methode wird auf die Reihe linearer Polyene des Typs H-(CH=CH) _N -H(2N7) angewendet (CNDO/2-Parametrisierung). Die excitonische Wellenfunktion wird bezüglich der Zellenpopulation und deren Schwankungen untersucht.

---

Résumé On prend la fonction d'onde excitonique déjà construite comme fonction d'onde d'ordre zéro pour l'état excité. L'interaction avec les autres déterminants monoexcités, les déterminants diet tri-excités est prise en considération par une perturbation au 2è ordre. Un choix judicieux de l'Hamiltonien non perturbé met en évidence d'importantes suppressions entre les séries de l'état excité et de l'état fondamental, et par conséquent le calcul direct des énergies de transition. Malgré le caractère multiconfigurationel de ₀, la localization complete des OM rend le calcul extrêmement rapide dans les hypothèses CNDO. La méthode est appliquée à la série des polyènes linéaires H-(CH=CH) _N -H (N = 2 à 7). Analyse de la fonction d'onde excitonique en terme de populations de loge et de leur fluctuations.

     

Multi-configuration electron-hole potential method for excited states

The recently proposed electron-hole potential (EHP) method for excited states is extended to the multi-configurational case. The variation equation is solved using the quadratic convergence method. The EHP methods are shown to be approximations to the complete singly excited configuration interaction (CSECI) in the variational sense. Extended Brillouin theorems are proved for the EHP methods. The excitation energies and wave functions obtained by one and two configurational EHP methods agree well with those of the CSECI method. The EHP methods have clear advantage in the computer time requirement over the CI method and are especially suited for a calculation of approximate excited states of large molecules. The EHP methods are applicable to excited states which belong to the same irreducible representation as the ground state.     

Generalized brillouin theorem multiconfiguration method for excited states

The Generalized Brillouin Theorem Multiconfiguration Method (GBT-MC) of Grein and Chang is extended and applied to the calculation of excited states. Orthogonality constraints to lower states as well as second-order interaction effects of states lying close together have been taken into account. In this way quadratic convergence can be guaranteed. Difficulties with coupling coefficients and Lagrangian multipliers of SCF methods can be circumvented. Test calculations have been performed on valence electron excited states of C, H₂O, and CH₂O, and on core excited states of Li.     

A modified PCILO method

The perturbative configuration interaction using strictly localized molecular orbitals, called the modified PCILO method, for which the use of the Rayleigh-Schrödinger many-body perturbation theory with the Moller-Plesset Hamiltonian partitioning is characteristic, has been proposed in this communication. On the CNDO/2 and INDO levels of Hamiltonian approximations strictly localized molecular orbitals have been constructed by solving modified Roothaan equations. From the zero and second order energy interatomic distances and harmonic force constants for some diatomic molecules have been calculated. The linear dependence of the correlation energy on the number of valence electrons in the series of the molecules CH₄, CH₃F, CH₂F₂, CHF₃ and CF₄ is perfect.     

Optimized effective potential method for individual low-lying excited states

This paper presents an optimized effective potential (OEP) approach based on density functional theory (DFT) for individual excited states that implements a simple method of taking the necessary orthogonality constraints into account. The amended Kohn-Sham (KS) equations for orbitals of excited states having the same symmetry as the ground one are proposed. Using a variational principle with some orthogonality constraints, the OEP equations determining a local exchange potential for excited states are derived. Specifically, local potentials are derived whose KS determinants minimize the total energies and are simultaneously orthogonal to the determinants for states of lower energies. The parametrized form of an effective DFT potential expressed as a direct mapping of the external potential is used to simplify the OEP integral equations. A performance of the presented method is examined by exchange-only calculations of excited state energies for simple atoms and molecules.     

An extended PCILO method

The perturbative configuration interaction using localized orbitals (the PCILO method) was extended in the way that current limitations to the two-centre bond approach were overcome. The localized molecular orbitals contain an arbitrary number of the basis set components; this follows from the a priori stated localized bonding model of a molecule. The extended PCILO method was formulated for the CNDO, INDO and NDDO Hamiltonian approximations. The configuration interaction was performed using the Rayleigh-Schrödinger many-body perturbation theory with the Møller-Plesset type of Hamiltonian partitioning, similar to that used in the so-called modified PCILO method. Applications to molecules with semi-localized and/or semi-delocalized bonds, as benzene or diborane, are presented.     

Test applications of a new SCF method for excited states

In order to test a recently proposed technique for deriving orthogonality-constrained HF wave functions for excited states, several applications to molecular systems, have been made and the results compared with those provided by other SCF techniques.     

Crystal calculation using the PCILO method

The PCILO method is used for the study of molecular systems with translational symmetry in a two-dimensional lattice. The calculation for the whole crystal is reduced to the calculation of unit cell pairs. By using the translational symmetry and the first-neighbour approximation, one shows that only four unit cell pairs have to be considered. The procedure described yields the ground-state energy and the charge distribution of the unit cell.     

Multiple bonds and excited states from the Hartree-Fock-Heitler-London method

The recently proposed Hartree-Fock-Heitler-London, HF-HL, method (Corongiu, G. J. Phys. Chem. A 2006, 110, 11584) previously tested for single bond molecules is validated by potential energy computations for open and closed shells, single and multiple bonds, in ground and excited states of homopolar diatomic molecules of the first and second period. The simple HF-HL function, including the configurations for 2s/2p near degeneracy and avoiding state crossing, yields correct dissociation products, qualitatively correct binding, and accounts for non-dynamical correlation. Addition of ionic structures improves the ab initio HF-HL function and yields about 95% of the experimental binding energies on average. Computed excitation energies are also in agreement with laboratory values as verified for the 3 Pi u and 3 Zeta g- excited states of the C2 molecule. Computation of the remaining dynamical correlation using a semiempirical functional yields binding energies with an average deviation of 1.5 kcal/mol from laboratory values, and total energies with an average deviation of 0.7 kcal/mol from exact nonrelativistic dissociation energies.     

Elongation method for calculating excited states of aromatic molecules embedded in polymers

Photophysical properties of polyethylene structures embedding aromatic fragments (benzene, anthracene, 4‐dicyanomethylene‐4H‐pyran, tryptophan, and estradiol) responsible for existence lowest electronically excited states were studied by new technique involving the elongation method applied to quantum‐chemical calculations. Absorption spectra and some photophysical properties were obtained. The comparison between the elongation and the conventional calculations was made, and it is shown that the elongation method is a powerful tool to determine the excited states as well as optical properties for large systems. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Effective local potentials for excited states

The constrained variational Hartree-Fock method for excited states of the same symmetry as the ground state [Chem. Phys. Lett. 287, 189 (1998)] is combined with the effective local potential (ELP) method [J. Chem. Phys. 125, 081104 (2006)] to generate Kohn-Sham-type exact-exchange potentials for singly excited states of many-electron systems. Illustrative examples include the three lowest (2)S states of the Li and Na atoms and the three lowest (3)S states of He and Be. For the systems studied, excited-state ELPs differ from the corresponding ground-state potentials in two respects: They are less negative and have small additional "bumps" in the outer electron region. The technique is general and can be used to approximate excited-state exchange-correlation potentials for other orbital-dependent functionals.     

Variational wavefunctions for low-lying excited states

The multiconfiguration method based on the generalized Brillouin theorem is well suited to optimize orbitals in variational wavefunctions for low-lying excited states of a given symmetry. Such wavefunctions are constrained to be orthogonal to and noninteracting with the wavefunctions for all lower states of the same symmetry. Test calculations were performed on the lowest excited ¹S state of Be. For a Hartree-Fock ground state wavefunction, singly excited configurations were insufficient to describe the lowest excited state, and triply excited configurations had to be added. For multiconfiguration ground state wavefunctions, however, singly excited configurations gave good results.     

Hall's variational principle for excited states

It is shown how excited state energies can be given upper bounds through the use of Hall's functional. Applications to atomic central field problems are worked out.     

An SCF technique for excited states

A method for deriving HF-SCF wave functions for excited states is presented here. All the active orbital transformations that are compatible with the orthogonality requirements are performed without unnecessary restrictions on the variational space and within a direct minimization approach. The method has been tested with an application on the first excited-singlet state of Be.     

The PCILO method at the INDO level

A new development of the PCILO method is presented for the INDO approximation. The new method allows the treatment of σ—π exchange phenomena and may be regarded as an improvement over the CNDO version.     

Hartree-fock calculations for excited rydberg states

A method is introduced which allows to compute self-consistent restricted Hartree-Fock wave functions for excited Rydberg configurations. The concepts of reorganization and electron correlation of Rydberg states are discussed. As an illustration Hartree-Fock calculations for the (ls)(nl) Rydberg series of He are presented.     

Density functional theory for excited states

In this article, we justify the use of standard Kohn-Sham (KS ) band structure theory for the calculation of the low-energy spectrum of metals and the density of states. For the higher spectrum, one can start the KS excited-state calculations by using as the first-order approximation the spin orbitals of the ground state. We next deal with the problem of degenerate states by using the subspace theory minimum principle. © 1995 John Wiley & Sons, Inc.