CNDO/INDO formalism for f block elements

The intermediate and complete neglect of differential overlap (INDO and CNDO /2) molecular-orbital theories are developed for molecules with f block elements in both the open- and closed-shell configurations.     

A CNDO/2 calculation on stilbene

The equilibrium conformations of trans- and cis-stilbene and the rotational barrier between the two isomers were calculated using the CNDO/2 method. The results for the equilibrium angles and distances are in good agreement with experimental data. However, according to the calculations the phenyl rings would have a nearly free rotation which is only limited by steric hindrance. This result obviously deviates from the current view. The results are discussed in relation to previous theoretical and experimental evidence.

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Zusammenfassung Die Gleichgewichtskonformation von trans- und cis-Stilben und die Rotationsbarriere zwischen zwei Isomeren wurde nach der CNDO/2-Methode berechnet. Die Ergebnisse in bezug auf die Geometrie stimmen mit experimentellen Daten gut überein, die Rotationsbarriere für die Drehung der Phenylringe dagegen ist praktisch Null.

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Résumé La méthode CNDO/2 a été employée pour calculer les conformations d'équilibre du trans- et du cis-stilbène ainsi que la barrière de rotation entre ces deux isomères. Angles d'équilibre et distances calculés sont en bon accord avec les données expérimentales. Cependant les calculs indiquent que les cycles phényles devraient posséder une rotation libre soumise seulement à l'empêchement stérique. Ce résultat s'écarte de l'opinion courante. Les résultats sont discutés en relation avec les données théoriques et expérimentales antérieures.

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This work was supported by grant No 2741-4 from The Swedish Natural Science Research Council and grant No 69-927/U 697 from The Swedish Board for Technical Development.     

Necessary conditions for the calculation of useful electrostatic isopotential maps from CNDO/INDO wavefunctions

The calculation of reliable electrostatic isopotential maps from CNDO or INDO wavefunctions while preserving the ZDO approximation fails because the individual atoms are treated as if they were spherical charge distributions. The resulting potential maps could be adequately interpreted on the basis of classical electrostatics. Approaches to the determination of useful maps include (a) the use of localized orbitals with a ZDO approximation applied among the localized orbitals as long as the localization procedure is defined with respect to the connectivity of the molecule and has no reference to a set of laboratory coordinates or (b) relaxation of the ZDO approximation in the determination of the potential by including the 3-center potential integrals. In either case, the preservation of rotational invariance takes paramount importance.     

An application of the CNDO/2 and INDO theories to the calculation of molecular quadrupole moments

Values of molecular quadrupole moments are calculated using the CNDO/2 and INDO methods and compared with experiment and other calculations. The agreement is good, except for π systems both linear and planar. Consideration of this disagreement suggests that use of π AO's which are less compressed perpendicular to the molecular plane or the internuclear axis may produce better results. A preliminary method of this type is adopted to obtain satisfactory theoretical results for π systems, too.     

A CNDO/INDO molecular orbital formalism for the elements H to Br. applications

The CNDO/INDO molecular orbital formalism introduced in the preceding paper has been applied to a large number of atom combinations up to bromine under the inclusion of the first transition metal series. The results are compared with experimental data (geometries, ionization potentials, dipole moments) or with the results of sophisticatedab initio calculations (one electron energies, net charges, atomic populations). The semiempirical model reproduces for a wide range of molecules the experimental andab initio data with remarkable success.     

The CNDO approximation in the Green's function method for VIP calculation

By introducing a CNDO adapted approximation into an appropriate irreducible interaction part a simple formula for calculation of vertical ionization potentials (VIP's) is derived. The method is applied to the molecules F₂, HF, C₂F₄, CH₂F₂, BF₃, CH₃F, CF₄.     

A CNDO/INDO molecular orbital formalism for the elements H to Br. theory

A CNDO and INDO formalism is presented that can be used for any atom combination up to bromine under inclusion of the first transition metal series. The semiempirical parameters were chosen to reproduce results ofab initio calculations on metalorganic compounds. The calculational results are invariant to rotations of the coordinate system but not to a general transformation into other basis functions. The one-center Coulomb-expressions were selected in order to include intraatomic correlation contributions. Within the CNDO model this could be achieved by the scaled monopole termF ₀, while in the INDO framework the one-center Coulomb integrals are given as a sum of the monopole-contributionF ₀ and higher multipole contributions expressed as a linear combination of Slater-Condon parameters. The invariance problem in the case of local rotations within the INDO approximation was solved by considering the combination of one-center Coulomb and exchange integrals as a function ofl but independent ofm. The two-center electron-electron interaction terms were calculated via the Dewar-Sabelli, Ohno-Klopman relation. Penetration effects were treated according to Fischer and Kollmar. For the resonance integralH _v ^AB parameters are used which carry information related to the directed nature of the chemical bond by using optimized Klondyke functions. The core-core repulsion is constructed as a superposition of a soft potential function, describing polarization effects of the atomic cores, and a hard repulsion function, avoiding the collapse of the atomic cores with decreasing distance.     

A CNDO/2 calculation of a rearrangement in cyclopentadienylsilane

The ground state geometry of cyclopentadienylsilane and the transition state geometry for SiH₃ group migration have been calculated by the CNDO technique, a semi-empirical version of the LCAO MO SCF approach.     

A CNDO/2 calculation on a complex between ethylene and chlorine

CNDO/2 calculations have been carried out for an ethylene chlorine complex, with the halogen orthogonal or parallel to the C-C bond. For comparison similar calculations were also carried out for ethylene and fluorine. The results are compared to estimates from experiments on related complexes and from Mulliken's resonance theory. It is concluded that the CNDO/2 calculations grossly overestimate the ethylene-chlorine interaction in particular if d-orbitals on chlorine are included in the AO-basis. The explanation for this may be the too high d-orbital exponent used here and the wrong asymptotic behaviour of the Slater orbitals.

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Zusammenfassung Es werden CNDO/2-Rechnungen für zwei Konformationen eines Äthylen-Chlor-Komplexes und eines Fluor-Analogens berichtet und die Resultate mit der Resonanztheorie von Mulliken und mit experimentellen Daten verglichen. Es ergibt sich, daß bei CNDO/2-Rechnungen die ChlorÄthylen-Wechselwirkung stark überschätzt wird, insbesondere, wenn d-Orbitale eingeschlossen werden. Letzteres könnte auch an einem großen Exponenten bei diesen Funktionen oder am falschen asymptotischen Verlauf von Slater-Funktionen liegen.

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Résumé Calculs CNDO/2 pour un complexe ethylène-chlore avec l'halogène orthogonal ou parallèle à la liaison C-C. A titre de comparaison des calculs analogues ont été aussi effectués pour l'éthylène et le fluor. Les résultats sont comparés à des estimations expérimentales sur des complexes voisins et à des estimations provenant de la théorie de la résonance de Mulliken. La conclusion est que les calculs CNDO/2 surestiment beaucoup l'interaction éthylène-chlore, en particulier lorsque l'on inclut des orbitales d dans la base des orbitales atomiques. La raison peut s'en trouver dans les exposants trop élevés des orbitales d et dans le mauvais comportement asymptotique des orbitales de Slater.

     

A CNDO and INDO calculation of nuclear spin-spin coupling constants in HF,HF 2 − and H2F 3 −

Two semiempirically SCF methods are used to calculate nuclear spin-spin coupling constants in hydrogen bonded systems. Hydrogen bonding is found to influence strongly the spin-spin coupling constants and this can give valuable informations about changes in electron densities with hydrogen bonding.     

Improved CNDO/S calculation of electronic spectra of organic compounds. I. New CNDO/S calculation by using an improved method of one-center electron repulsion integral

The NM-gamma CNDO/S program previously developed by our group was modified by the introduction of a new one-center electron repulsion integral gamma(AA)(new) approximation, namely, the gamma(AA)(new)-CNDO/S method. The value of this gamma(AA)(new) was evaluated according to the product values of the coefficient C with the gamma(AA) value proposed in our previous paper. This method using a new gamma(AA) was also found to improve the two-center electron repulsion integral gamma(AB) value with respect to the chemical softness proposed by Nishimoto and co-workers, together with the difference between HOMO and LUMO orbital energies. The results calculated by the present improved gamma(AA)(new)-CNDO/S method demonstrated that not only the calculated absorption maxima wavelengths and ionization potentials, but also the order and the assignment of orbitals coincided very well with those based on the results of experiments investigating a variety of polyenes, cyanynes, and polycyclic aromatic hydrocarbons.     

CNDO,INDO and RCNDO-CI calculations on the electronic spectra of saturated hydrocarbons

CNDO, INDO and RCNDO (CNDO including higher (Rydberg) atomic orbitals in the basis) calculations completed by first order configuration interaction were performed on straight chain and branched chain paraffins.The results interpret reasonably the main characteristics of the observed electronic spectra. The importance of outer atomic orbitals is stressed and it is found that the first singlet-singlet transition of highly branched paraffins leads to an excited state with considerable Rydberg character.

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Zusammenfassung Rechnungen vom Typ CNDO, INDO und RCNDO (CNDO mit höheren (Rydberg) Atomorbitalen in der Basis) unter Einschluß von Konfigurationswechselwirkung 1. Ordnung wurden für unverzweigte und verzweigte gesättigte Kohlenwasserstoffe durchgeführt.Die Resultate lassen eine Deutung der Hauptcharakteristika der beobachteten Elektronen-spektren zu. Die Wichtigkeit der äußeren Atomorbitale ist zu betonen. Die ersten Singulett-Singulett-Übergänge der stark verzweigten Paraffine führen zu angeregten Zuständen mit beträchtlichem Rydbergcharakter.

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Résumé Des calculs CNDO, INDO et RCNDO (ayant des orbitales atomiques supérieures dans la base) ont été effectués sur les paraffines normales et ramifiées tenant compte de l'intéraction de configuration de premier ordre jusqu'à 30 configurations.Les résultats interprêtent d'une manière raisonnable les spectres électroniques mesurés. L'importance des orbitales atomiques supérieures apparaît clairement. La première bande observée des hydrocarbures hautement ramifiés comme le néopentane ou l'isobutane est attribuée à une transition dont l'état excité possède un fort caractère Rydberg.

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The research for this paper was supported in part by the Defense Research Board of Canada; Grant Number 9530-63.     

A Crystal Orbital approach for two- and three-dimensional solids on the basis of CNDO/INDO Hamiltonians. Basis equations

A Hartree–Fock (HF ) self-consistent field (SCF ) crystal orbital (CO ) formalism for two- and three-dimensional (2D/3D) solids on the basis of semiempirical CNDO /INDO (complete neglect of differential overlap; intermediate neglect of differential overlap) Hamiltonians is presented. The employed SCF variants allow for the treatment of atomic species up to bromine under the inclusion of the first (i.e., 3d) transition metal series. Band structure investigations of 2D and 3D materials containing more than 30 atoms per unit cell are feasible by the present SCF HF CO formalism. The theoretical background of the computational scheme is given in this contribution. Special emphasis is placed on physically reliable truncation criteria for the lattice sums, the adaptation of the crystal symmetry in k space, as well as the suitable choice of domains in Brillouin zone (BZ ) integrations required in the determination of charge-density matrices. The capability and limitations of the semiempirical SCF HF CO approach is demonstrated for some simpler solids by comparing the present computational results with those of ab initio CO schemes as well as conventional numerical methods in soid-state theory. The employed model solids are graphite and BN (2D and 3D networks for both solids) as well as diamond, silicon, germanium, and TiS₂.     

2-取代吡啶衍生物的CNDO/2计算和分子光谱研究

本文用CNDO/2方法计算了吡啶及其2-取代衍生物,测了其紫外光谱.通过红外,紫外光谱和量子化学计算的综合分析,确定2-吡啶酮与2-羟基吡啶是互变异构体,并推断2-氨基吡啶的互变异构体存在,从而很好地得到了此系列紫外光谱的线性规律.     

Unrestricted Hartree-Fock instabilities in semiempirical CNDO/S and INDO/S calculations of spin-spin coupling constants

It is shown that non-convergent calculations of the Fermi contact term of spin-spin coupling constants within the self-consistent and finite perturbation schemes used to solve the coupled Hartree-Fock equations, are originated in non-singlet Hartree-Fock instabilities of the closed-shell restricted Hartree-Fock wavefunction. In CNDO/S and INDO/S wavefunctions, where the electronic system response has been successfully reproduced, all investigated molecules containing MOs were found to be unstable. Results of spin-spin coupling constants are given and compared with experimental as well as FP and SOS INDO values.Part of a Ph.D. thesis (G.E.S.) to be presented to the University of Buenos Aires.Comisión de Investigaciones Científicas (CIC, Pcia. de Bs. As.) fellow.     

The effect of σ and π singly-excited configurations in the calculation of excited states by the CNDO and INDO approximations

The CNDO/2 and INDO approximations (with their original parametrization) are utilized for the calculation of transition energies. The effect of including all ( and ) singly excited configurations is assessed in C₂H₄, H₂CO, HCOOH and HCONH₂, and the results are compared to experimental transitions and to the available non-empirical calculations. The effect of extensive mixing is then considered in larger molecules.

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Zusammenfassung Die Näherungen CNCO/2 und INDO (mit ihrer ursprünglichen Parametrisierung) werden für die Berechnung von Übergangsenergien benutzt. Der Effekt des Einschlusses aller ( und ) einfach angeregter Konfigurationen wird untersucht für C₂H₄, H₂CO, HCOOH und HCONH₂ und die Ergebnisse werden mit experimentellen Übergängen und den verfügbaren nicht-empirischen Rechnungen verglichen. Die Überlegungen werden dann auf größere Moleküle ausgedehnt.

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Résumé Les procédés CNDO/2 et INDO (avec leur paramétrisation originale) sont utilisés pour calculer des énergies de transition. L'effet du mélange de toutes les configurations monoexcitées ( et ) est étudié pour C₂H₄, H₂CO, HCOOH et HCONH₂, les résultats sont comparés aux transitions expérimentales et aux calculs non-empiriques disponibles. L'étude est étendue à de plus grandes molécules.

     

A CNDO/INDO crystal orbital model for transition metal polymers of the 3d series—basis equations

The crystal orbital formalism in the tight-binding approximation is combined with a recently developed CNDO/INDO model for transition metal species of the 3d series in order to allow band structure calculations on the Hartree-Fock (HF) SCF level for one-dimensional (1D) chains with organometallic unit cells. The band structure approach based on the CNDO and INDO approximation can be used for any atom combination up to bromine under the inclusion of the 3d series. The matrix elements for the tight-binding Hamiltonian are derived for an improved CNDO and INDO framework. The total energy of the 1D chain is partitioned into one-center contributions and into two-center increments of the intracell and intercell type. Semiempirical band structure calculations on simple model systems are compared with available ab initio data of high quality.     

A CNDO calculation of ring medels of polywater

Taking the calculated energy as a criterion, the ring consisting of six H₂O units with protons placed in the middle between oxygen appears more stable than the four-membered one. The distance of the extracyclic protons is very important. The charges on the atoms are small.