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.     

A complete diagrammatic construction of PCILO method

In the present short communication, the diagrammatic many-body perturbation theory for the rederivation of PCILO method (perturbation configuration interaction using localized orbitals, see Theoret. Chim. Acta (Berl.)13, 1 (1969) and15, 100 (1969)) is consequently used. Using the Goldstone-Hugenholtz linked-cluster theorem, the diagrammatic expression for the exact ground-state energy is obtained. An application of the present approach to the low-lying excited and/or ionized states is also discussed.     

A steepest-descent method for the calculation of localized orbitals and pseudoorbitals

A method for direct calculation of localized non-orthogonal orbitals, which has been proposed by the authors recently, is extended to cases where the overlap between different subsystems is very large. This is achieved by using a steepest-descent procedure. In addition, a computationally simple treatment of correlation effects is introduced into the method by means of the density functional formalism. Results of the method are given for e.g. LiH, CH₄, Ne₂, CO,(FH)₂.     

Quadratically convergent calculation of localized molecular orbitals

Two iterative procedures for the transformation of canonical self-consistent field molecular orbitals to intrinsic localized molecular orbitals are proposed. A first-order method based on a series of (n × n) unitary transformations may be applied to orbitals which are far from convergence. The second method, based on Newton's method, yields quadratic convergence. Numerical results based on Boys' criterion are presented for water, carbon monoxide, boron fluoride, nitric oxide, and methylacetylene. A composite method may be used to obtain rapid convergence for large molecules for which it is not practical to calculate the entire hessian matrix. The performance of the composite method is demonstrated by application to the dinitrogen tetroxide molecule. Highly converged localized molecular orbitals may be obtained for most molecules with five to eight first-order iterations followed by three or four iterations based on either the second-order or composite method.     

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 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.     

L'utilisation d'orbitales localisées dans l'étude théorique des molécules

The five simplest alkanes have been studied in terms of localized orbitals. The transferability of the Fock matrix elements in this basis allows us to elaborate a simple parametric procedure adapted for saturated hydrocarbons. Some original applications of this procedure are performed.

     

An analysis of the complex molecular orbitals method

Numerical results for the ground state of the HN ₂ ⁺ and HCO⁺ molecular ions at their near equilibrium geometry, obtained by the complex molecular orbitals (CMO) method in the extended basis set, are reported. The CMO wavefunction of the HN ₂ ⁺ ion is compared with the CI wavefunction obtained in the same basis set. This reveals the nature of approximations inherent in the CMO method. A peculiar feature of the occupation numbers of the CMO natural orbitals is also explained.Alexander von Humboldt Fellow. On leave from the Institute Rudjer Bokovi, Zagreb, Croatia, Yugoslavia.     

Orbital localization in transition metal molecules

In multiply bonded, weakly interacting systems the excessive electron repulsion associated with the non-dynamical correlation error can be reduced within the Hartree Fock approximation by localizing the bonding orbitals. The mechanism behind this (unphysical) orbital localization is studied through calculations on a model system, and SCF and CI calculations on the MnO⁺ ion. It is shown, from a pair-population analysis of the two-particle density matrix (which is analogous to a Mulliken population analysis of the one-density) that the orbital localization is a two-electron effect. Transition metal molecules often exhibit this kind of orbital localization which may (or may not) require symmetry breaking. The special characteristics of transition metal molecules that makes them suitable candidates for orbital localization will be discussed.     

On the direct calculation of localized HF orbitals in molecule clusters,layers and solids

It is shown that the computational effort involved in HF calculations can be considerably reduced by applying the following concepts: 1) the use of a localization operator for the direct determination of localized non-orthogonal HF orbitals, 2) the approximation of the interaction potential between different localization centres by a Hartree-like ansatz, 3) the successive calculation of many-body corrections to molecular properties such as the total energy. A numerical application to LiH layers and solid LiH is described.     

Superior performance of Mukherjee’s state-specific multi-reference coupled-cluster theory at the singles and doubles truncation scheme with localized active orbitals

The state-specific multi-reference coupled-cluster (SS-MRCC) theory of Mukherjee et al., in its singles and doubles truncation scheme (SS-MRCCSD), misses important couplings between the virtual functions reached by single and double excitations from different model functions. Since the SS-MRCC theory is not invariant with respect to the transformations among the active orbitals, the results are dependent on the active orbitals chosen. We demonstrate in this paper with results for potential energy curves for several example molecules involving single and multiple bond dissociation that the performance of SS-MRCCSD is significantly improved if localized active orbitals are used. The improvement is remarkable both in terms of the non-parallelity error and the magnitude of correlation energy recovered vis-a-vis the full configuration interaction results with the same basis set. The results bolster our claim that SS-MRCCSD with localized orbitals is an accurate general theory for potential energy surfaces.     

PCILO method for excited states

In the scope of building a PCILO method for excited states, one builds and tests excitonic zeroth order wave-functions. For \(\left( {_\pi ^{\pi ^ * } } \right)\) transitions, the (σ+π) excitonic and purely (π) excitonic wave functions are compared, showing that theσ-π coupling between \(\left( {_\pi ^{\pi ^ * } } \right)\) and \(\left( {_\sigma ^{\sigma ^ * } } \right)\) single excitations may be considered as a perturbation. The excited state wave-functions are analyzed in terms of neutral and ionic structures, and the fluctuation of the charges in the two-electrons loges are studied, showing that theσ-π coupling favours the neutral structures and diminishes the charge-fluctuations.     

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.

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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.

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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.

     

Orbital Energy Order and the Through Bond Interaction in Homonuclear Diatomic Molecules

The homonuclear diatomic molecules are the simplest systems having both the σ framework and the lone pair orbitals n_a and _b for investigating their through space and through bond interaction. The striking orbital energy order n_g～ n_a+ n_b > n_n ～ n_a - n_b has been accounted for by the through bond interaction. However, when the p-content in the lone pair orbitals n_a and n_b decreases, one may have the reverse orbital energy order: n_g < n_g. A reverse orbital energy order has been found in F₂ and Cl₂, whose n_a and n_b are almost pure s-type atomic orbitals. The reverse order also occurs in molecule N₂ when the internuclear distance is larger man 1.5 Å. It is also found that the detail through space and through bond interaction and the eventual orbital energy order for n_g and n_u can be accounted for by the Fock operator within the localized molecular orbital space.     

Application of the many-body perturbation theory to normal saturated hydrocarbons in the localized representation

The second-order energy corrections are calculated for some normal saturated hydrocarbons by using the many body-perturbation theory (MBPT) based on localized orbitals. The correlation energies are expressed as the sum of contributions from virtual orbital pairs. We have found that these contributions are transferable and have interesting structural features: the trans-coplanar effects are relatively large. Partitioning the correlation energies according to the order of neighbourhood we have found that the zero order effects are the largest but the first and second neighbour contributions are also important.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

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.     

双核钼硫原子簇顺反异构体的定域化分子轨道研究

本文对簇合物离子[Mo_2(μ-S)_2S_2(S_2C_2H_4))_2]~(2-)的顺式和反式异构体进行了CNDO定域化计算,讨论了它的两种异构体的化学键性质,特别是Mo—Y(S)间的三重键性质.探讨了用亚层Mulliken布居数分析键的性质的可能性,并说明了这类簇离子多以顺式异构体存在的原因.     

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.     

Lien元素簇合物的成键作用

镇元素簇合物是人们最感兴趣的簇合物之一l‘－’］．已有的。作主要是研究它的稳定性和电子结构，对其成键性质还研究得不多·为止匕我们对Lkin为元素簇合物中所含原子个数，e为该化合物的电荷）进行了定域化研究，并得出一些有意义的结果·1计算我4rl采用GAMESS90程序m，在4－31G基组下进行了正则分子轨道SCFi十算（闭壳层采用RHF，开壳层采用UHF）．然后，以QSU90程序问，用B0yS方法进行了定域化计算，得到定域分子轨道（LM），再根据LMO的系数和集居数分析，判断各分子中原子的成键情况问．共计算了18个簇合物．它们的原子数…