Localized bond orbitals and the correlation problem

A method is proposed to go beyond the SCF result in the calculation of the ground state energies without any variational procedure. One chooses a set of reasonable bonding and antibonding orbitals localized on the chemical bonds. The bonding orbitals are used to built a fully localized determinant. The basis of excited states is built using the antibonding orbitals. One calculates the lower eigenvalue of the CI matrix in this basis by a Rayleigh-Schrödinger expansion. The conceptual and practical advantages of the method are discussed, and the perturbation series is specified in order to satisfy the linked cluster theorem conditions and to retain the advantages of the Epstein-Nesbet partition of the Hamiltonian.

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Zusammenfassung Es wird eine Methode angegeben, die die SCF-Resultate in der Berechnung der Grundzustandsenergien übertrifft, ohne die Mittel der Variationsrechnung anzuwenden. Als Basisfunktionen wählt man einen Satz geeigneter bindender and antibindender Orbitale, die auf den chemischen Bindungen lokalisiert sind. Die bindenden Orbitale werden zum Aufbau einer völlig lokalisierten Determinante benutzt. Als Basisfunktionen für die angeregten Zustände benutzt man auch antibindende Orbitale. Man berechnet den tieferen Eigenwert der CI Matrix mit dieser Basis durch eine Rayleigh-Schrödinger- Entwicklung. Die begrifflichen und praktischen Vorteile dieser Methode werden diskutiert. Indem man die Störungsreihe so wählt, daß das linked cluster-Theorem erfüllt ist, bleiben die Vorteile der Epstein-Nesbet-Aufspaltung des Hamiltonoperators erhalten.

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Résumé On propose une méthode pour dépasser la valeur SCF dans le calcul de l'énergie de l'état fondamental en évitant tout procédé variationnel. On choisit un jeu raisonnable d'orbitales liantes et antiliantes sur les liaisons chimiques. Le déterminant totalement localisé est bâti à l'aide des orbitales liantes. Les orbitales antiliantes servent à construire les états excités, base de la matrice d'Interaction de Configuration. La plus basse valeur propre de celle-ci est développée par perturbation. Les avantages conceptuels et pratiques de la méthode sont discutés. On précise une série de perturbation qui permet de combiner les avantages du théorème du linked cluster et de la partition Epstein-Nesbet de l'Hamiltonien.

     

Localized bond orbitals and the correlation problem

The stability of the results of the Perturbative Configuration Interaction using Localized Orbitals (PCILO) with respects to the choice of the hybrids and to the bond polarities is studied for several small strained molecules. The stability of 2^nd and 3^rd orders is quite satisfactory. The pertinence of the maximum overlap criterion to build hybrids is discussed.

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Zusammenfassung An verschiedenen kleinen Ringen wird die StabilitÄt der Ergebnisse einer Störungs-CI-Rechnung studiert, wobei bezüglich der Wahl der Hybride und der BindungspolaritÄten lokalisierte Orbitale benutzt werden. Die StabilitÄt der Ergebnisse für Störungen 2. und 3. Ordnung ist zufriedenstellend. Das Kriterium der maximalen überlappung zum Aufbau von Hybriden wird diskutiert.

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Résumé On étudie la stabilité des résultats de la méthode: Développement Perturbatif de la matrice d'Interaction de Configuration en base d'Orbitales de Liaison (PICOL) par rapport aux paramétres qui déterminent les orbitales de liaison hybridation et polarité pour plusieurs petites molécules contraintes. La stabilité aux 2é et 3é ordres est assez bonne. On discute les rapports du critére de Recouvrement Maximum avec les problémes énergétiques.

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NATO postdoctoral fellow

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Associé au CNRS.     

Localized orbitals and the Fermi hole

The relationship between localized orbitals and the Fermi hole is demonstrated with contour maps of the Fermi hole in the water molecule. These contour maps indicate the presence of regions in which the Fermi hole is relatively stable, regions in which the shape of the Fermi hole changes rapidly, and regions in which the Fermi hole follows the probe electron smoothly. If a single orbital dominates any region of space, the Fermi hole resembles that orbital for any position of the probe electron in the dominated region.     

Localized virtual and occupied molecular orbitals

This report describes the generation of localized from canonical molecular orbitals such that the method (1) be consistently applicable to occupied bond, lone pair and unoccupied orbitals and (2) permit symmetry related orbitals in molecules of two-fold or higher symmetry. Minimization of populations completely external to each local pair region effectively meets these criteria. Finally, conventional strategy for finding the global extremization point is costly in time and memory to implement; a much more efficient numerical search procedure for the global extremum is described. Results for ethylene, butadiene and benzene are presented to clarify the difficulties and their resolution.     

Localized orbitals based on the fermi hole

The Fermi hole provides a direct (non-iterative) method for tansforming canonical SCF molecular orbitals into localized orbitals. Except for simple overlap integrals required to maintain orthogonality, this method requires no integrals over orbitals or basis functions. This method is demonstrated by application to a furanone (C₄H₄O₂), methylacetylene, and boron trifluoride. The results of these calculations are compared to those determined by the orbital centroid criterion of localization.     

Localized orbitals in hydrogen bonded systems

The localized molecular orbitals for a variety of hydrogen bonded systems are obtained from their INDO and CNDO/2 wavefunctions. The bonding of these systems is qualitatively discussed in light of the localized orbitals.     

Localized molecular orbitals for polyatomic molecules

Molecular wavefunctions have been generated by the PRDDO (Partial Retention of Diatomic Differential Overlap) method for the monocyclic aromatic rings containing six π-electrons (C₄H ₄ ^?2 , C₅H ₅ ^? , C₆H₆, C₇H ₇ ⁺ , and C₈H ₈ ⁺² ) and ten π-electron species (C₈H ₈ ^?2 , C₉H ₉ ^? , C₁₀H₁₀). The eigenvalue spectra of the canonical molecular orbitals are presented. Localized molecular orbitals (LMO's) generated using the Boys criterion are reported for localizations involving all occupied molecular orbitals (complete localizations) and localizations of the π orbitals only. We find evidence for σ-π separation in the complete localizations for some of these molecules even though the Boys criterion is often biased against such results. We demonstrate for C₆H₆ and find for the other molecules that the π-orbital localizations are indeterminate (i.e. there are an infinite number of equally satisfactory LMO structures between two limiting extremes). This result may be viewed as a corollary of Hückel's (4n+2) rule for aromaticity.     

Localized molecular orbitals for aromatic molecules

Localized molecular orbitals are calculated using the method of Boys for the aromatic molecules C₆H₆, C₆H₅X and the p-, m-, and o-forms of C₆H₄XY, where X,Y = CN,OH,F. The calculations are performed both with and without the constraint of σ, π-separation in the localization. The localized π-orbitals are multicenter bonds. If the σ- and π-orbitals are localized together, two different structures are found, Kekulé-type structures and structures with a set of six two center and a set of three three center bonds. The C-X bond turns out to be a single bond if X = CN and a double bond, if X = OH or F.     

Localized orbitals for the oxygen and nitric oxide molecules

Localized orbitals are derived for the ground states of the oxygen and nitric oxide molecules by applying localization methods separately to the orbitals containing electrons of alpha- and betaspin. Both the intrinsic energy localization and the uniform localization methods are used. The resulting localized orbitals are in good agreement with the formulae suggested by Linnett.

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Zusammenfassung Für die Grundzustände der Moleküle O₂ und NO werden lokalisierte Orbitale abgeleitet, indem die Lokalisierungsmethoden getrennt für die Orbitale mit- und-Spin angewendet werden. Dabei werden sowohl die eigentlichen Energielokalisierungsmethoden als auch die gleichförmigen Lokalisierungsmethoden benutzt. Die erhaltenen lokalisierten Orbitale stimmen gut mit den von Linnett vorgeschlagenen Formeln überein.

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Résumé Obtention d'orbitales localisées pour l'état fondamental des molécules d'oxygène et d'oxyde nitreux par localisation indépendante des orbitales de spin et des orbitales de spin. Emploi simultané de la localisation selon l'énergie intrinsèque et de la localisation uniforme. Les orbitales localisées résultantes sont en bon accord avec les formules suggérées par Linnett.

     

Localized orbitals for the description of molecular interaction

The intermolecular interaction between the molecules CH₂O and NH₃ was investigated by the supermolecule method. The interaction energies were first calculated at the ab initio SCF level, and the electron correlation was included via second-order Møller-Plesset perturbation theory (MP 2). The basis set superposition error (BSSE ) was taken into account by the counter-poise (CP ) method. The occupied and the virtual canonical molecular orbitals (CMOS ) of the supermolecule were separately localized by the Boys' procedure. The correlation correction was calculated by the many-body perturbation theory (MBPT ) in the localized representation. Contributions of the third- and fourth-order localized diagrams were added to those of the second-order canonical diagram. This procedure gives a correction nearly equivalent to that of MP 2. The possibility to separate LMO contributions responsible for the dispersion interaction was investigated.     

Maximum bond order hybrid orbitals

Summary Based on the simplified calculation scheme of the maximum bond order principle and the basic idea of the maximum overlap symmetry orbital method, a simple procedure is suggested for constructing systematically the bonding hybrid orbitals, called maximum bond order hybrid orbitals, for a given molecule from the first-order density matrix obtained from a molecular orbital calculation. As an example, the proposed procedure is performed for some typical small molecules by use of the density matrix obtained from CNDO/2 calculation. It is shown that the bonding hybrid orbitals constructed by using the procedure are extremely close to those by using the natural hybrid orbital procedure and in good agreement with chemical intuition, and that the proposed procedure can be performed more easily than the natural hybrid orbital procedure and can given simultaneously the values of the maximum bond order for all bonds in molecules.The project was supported by National Natural Science Foundation of China and also supported partly by Foundation of Hubei Education Commission     

Localized orbitals for optimal decomposition of molecular properties

We present the procedure for transforming delocalized molecular orbitals into the localized property-optimized orbitals (LPOs) designed for building the most accurate, in the Frobenius norm sense, approximation to the first-order reduced density matrix in form of the sum of localized monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one-electron properties derived from the original many-electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open-source freeware program JANPA ( http://janpa.sourceforge.net /) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree-Fock and second-order Moller-Plesset theory levels and excellent agreement with the chemist's Lewis-structure picture is found.     

Orthogonalized atomic orbitals and the interpretation of valence bond wavefunctions

The use of orthogonalized atomic orbitals in valence bond type wavefunctions is critically examined. By analyzing a test case in detail, it is shown that the simple interpretation of such wavefunctions in terms of weighted chemical formulae can be misleading.     

Localized molecular orbitals and chemical binding in five-membered heterocycles. II

The localized molecular orbitals (LMOs) of thiophene, furan, and pyrrole are derived from ab initio 4-31G wavefunctions using Boys' criteria for localization. From the transferability point of view, these LMOs are classified as (i) completely different and nontransferable LMOs (these are the lone-pair orbitals on O and N on one hand and those on S on the other hand), (ii) chemically similar lone pairs and inner shells on O and N (of furan and pyrrole, respectively), and (iii) chemically equivalent C? C, C?C, and C? H LMOs in the three heterocycles. The sp³ hybridization of the L core of sulfur, its appreciable polarization, and considerable involvement in bonding in the C? S bond region have been discussed. The present investigation indicates the limitation of the application of semiempirical MO methods to molecules that contain second-row atoms due to both the appreciable core—valence and π-σ interactions involving such atoms. Qualitative investigation of aromaticity and reactivity of the studied heterocycles agrees satisfactorily with experimental observations and shows that conclusions drawn based solely on static factor considerations (charge distribution in the noninteracting molecules) might very well be misleading and such factors determine the ease rather than the final orientation of the substituent.