Showing papers in "Theoretical Chemistry Accounts in 1969"

Localized bond orbitals and the correlation problem

Abstract: Formulas are given allowing the calculation of electronic molecular energy up to the third-order in a perturbation theory using fully localized bond orbitals with zero differential overlap between them. The method is applied to small molecules using the CNDO approximations of Pople and Segal.

Porphyrins XIV. Theory for the luminescent state in VO, Co, Cu complexes

Abstract: The normal triplet state of closed shell metal porphyrins becomes a “tripdoublet” and a quartet in systems with one unpaired d electron. Exchange integrals between metal d and porphyrin π-electrons give intensity to the tripdoublet and set the tripdoublet-quartet energy gap. These integrals are evaluated theoretically giving tripdoublet radiative lifetimes between 26 and 1450 μsec and tripdoublet-quartet energy gaps in the range 156 to 639 cm−1 for the metals and porphyrin skeletons considered. Spinorbit coupling similarly gives intensity to the quartet and causes a zero field splitting dependent on a parameter Z which has value 0.7, 3.5, 20.4, 21.6 cm−1 for Zn (triplet), Cu, Co and VO complexes. Theory predicts that the intensity ratio of 0−1 to 0−0 bands will be very low for the tripdoublet but stronger for the quartet. Existing experimental evidence shows that luminescence comes from both the tripdoublet and the quartet states, their relative importance varying with metal, porphyrin skeleton, and temperature.

Ab initio Calculations on cytosine, thymine and adenine

Abstract: An ab initio LCAO SCF calculation has been performed in a small contracted GTO basis set on three bases of ADN. A check of the representativity of the basis set is reported for formamide and pyrrole.

Localized bond orbitals and the correlation problem: IV. Stability of the perturbation energies with respect to bond hybridization and polarity

Abstract: 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 2nd and 3rd orders is quite satisfactory. The pertinence of the maximum overlap criterion to build hybrids is discussed.ZusammenfassungAn 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.RésuméOn 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.

A reparametrization of the CNDO method I. Hydrocarbons

Abstract: The empirical evaluation of the core matrix elements in the CNDO method is modified and the parameters are adjusted to give optimal values for heats of atomization, bond lengths, bond angles and force constants.

SCF MO calculations of heteroatomic systems with the variable Β approximation

Abstract: In order to elucidate the electronic structure of protonated N-heterocycles, we have carried out SCF MO calculations, considering the σ-bond polarizations which are caused by the large net charge on nitrogen atom. Appropriate parametrizations of the valence state energies associated with the σ-bond polarization model have been proposed. Our calculations showed that a conventional covalent model for protonated N-heterocycles failed to explain the experimental electronic spectral data and an extremely polarized σ-core model gave quite good results in the whole. The present theory expected that the nature of electronic spectra of quinoline is considerably changed by the σ-bond polarization due to the protonation.

Hartree-Fock-Roothaan wave functions, electron density distribution, diamagnetic susceptibility, dipole polarizability and antishielding factor for ions in crystals

Abstract: Using the Hartree-Fock method the wave functions of Li+, Be2+, O2−, F−, Na+, Mg2+, Al3+, S2−, Cl−, K+, Ca2+, Sc3+ and Ti4+ have been calculated for the free ion and the ion in a potential well. The main result of these calculations is a contraction of the anion and an expansion of the cation due to the external potential. A comparison of the calculations with an experimental determination of the electron density distribution in NaCl and MgO shows qualitative agreement. The diamagnetic susceptibility χ, the dipole polarizability αd, and the Sternheimer antishielding factor γ∞ of the ions given above were also calculated for the free ions and the “spherical potential” ions (SPI). The charged hollow sphere model improves the theoretical values towards the properties determined by experiment.

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

Abstract: The CNDO/2 and INDO approximations (with their original parametrization) are utilized for the calculation of transition energies. The effect of including all (σ and π) 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.

Semiempirical quantum mechanical studies on some hydrogen bonded systems

Abstract: The CNDO/2 method is used to study the hydrogen bond strength in several representative systems. Enthalpies of hydrogen bond formation are generally predicted fairly well although some exceptions are noted. The proton-proton acceptor distances are predicted to be about 10 percent too small in all cases where comparison with experiment can be made.

Hydrogen bonding: A molecular orbital treatment by the EHT and the CNDO/2 methods of methanol and of formic acid

Abstract: By both the EHT and the CNDO/2 calculations, the linear dimer of methanol is found to be more stable than the cyclic dimer. The hydrogen bonds in the trimer are stronger than those in linear dimers. The proton potential function, charge densities, and overlap populations in the linear dimer of methanol have been obtained. The CNDO/2 calculations show that the cis-form of formic acid is more stable than the trans-form, in agreement with experimental data. The cyclic dimer of formic acid is more stable than the open dimer. The β-form of formic acid trimer is more stable than the α-form. The proton potential function and the charge densities in the cyclic dimer of formic acid have been obtained. The CNDO/2 method gives more realistic proton potential functions for the dimers of methanol and formic acid. The O ... O stretching force constant in the dimers of methanol and formic acid have been estimated to be 0.13 × 105 dynes/cm and 0.27 × 105 dynes/cm, respectively, in agreement with experimental data.

Analyse conformationnelle théorique III. Etude ab initio SCF-LCAO-MO de l'inversion de l'azote dans l'Aziridine et dans l'Oxaziridine

Abstract: Une etude theorique des barrieres d'inversion de l'azote dans l'aziridine et dans l'oxaziridine a ete effectuee dans le cadre de la methode ab initio SCF-LCAO-MO. — Les barrieres d'inversion calculees sont de 18,3 kcal/mole pour l'aziridine et de 32,4 kcal/mole pour l'oxaziridine. Ces barrieres, ainsi que d'autres proprietes moleculaires, sont en bon accord avec les valeurs experimentales. — L'analyse des resultats fournit une image physique de l'origine des barrieres d'inversion et des effets des heteroatomes.

Inclusion of 3d orbitals in calculations involving second row atoms

Abstract: Valence-state ionisation potentials, I Μ , and non-empirical one-centre electron repulsion integrals are evaluated for the separate 3s, 3p and 3d orbitals of Na, Mg, Al, Si, P, S, and Cl. These parameters are for use in the application of the CNDO SCMO method to molecules containing second row atoms.

Elektronenwellenfunktionen und Terme zweiatomiger Moleküle bei großen Atomabständen

Abstract: Es wird ein systematisches Verfahren zur Berechnung von Matrixelementen Der Elektronenenergie fur Systeme aus zwei wechselwirkenden Atomen angegeben, bei festem, grosem Abstand. Im Wechselwirkungsoperator werden Spin-Bahnkopplung, Polarisation und Austausch berucksichtigt. Als Basisfunktionen werden Molekulfunktionen der Kopplungstypen „a“ und „c“ nach Hund verwendet. Atome mit unabgeschlossenen p-Schalen werden besonders sorgfaltig untersucht.

Electronic structures of aromatic amine N-oxides

Abstract: The electronic structures of heterocyclic amine N-oxides, nitrones, and nitrile N-oxides were systematically studied by the Pariser-Parr-Pople method. In addition, the intensity of n- π * transition pertinent to conjugated N-oxide systems has been calculated. The results of these calculations were compared with the experimental ones reported hitherto and also carried out in the present work. The electronic structure and spectra of aromatic amine N-oxides were thus discussed in detail.

Uncoupled Hartree-Fock calculations of the ring current contribution to the chemical shifts in conjugated hydrocarbons

Abstract: Uncoupled Hartree-Fock perturbation theory is adapted for the calculation of the ring current contribution to the chemical shifts in a number of conjugated hydrocarbons. The results compare favourably with those of the coupled form of the theory. It is also shown that the Huckel approach may be modified so as to give values close to those of the SCF theory.

Gaussian expansions of minimal STO basis for calculations in molecular quantum mechanics

Abstract: By means of minimal basis SCF calculations for HF, H2O, NH3 and CH4 different expansions of Slater orbitals (STO) in terms of Gaussian orbitals (GTO) are tested in order to find an appropriate compromise between sufficient accuracy of the results and reasonable computing times. The least squares fit of the GTO expansion to STO does not appear to have any advantages over the expansion based on a variational procedure. It turns out that for hydrogens an expansion of the 1s orbital in terms of three GTO is quite sufficient, whereas for first row atoms an expansion of the 1s orbital in terms of three to five GTO, of the 2s orbital in terms of two GTO and of the 2p orbitals in terms of three GTO seems to be adequate.

The electronic structure of cyclopropane, cyclopropene and diazirine an ab initio SCF-LCAO-MO study

Abstract: The electronic structure of cyclopropane, cyclopropene and diazirine has been studied within the ab-initio SCF-LCAO-MO theoretical framework. The present results lead to a general bonding model for three-membered ring systems. Composition of the MO's, population analyses and electron density distribution diagrams were used to establish the nature of the bonding. The total electron density distributions in cyclopropane and in cyclopropene lead to a “bent bond” + “central hole” bonding model; however the bending angle is only ca. 5° and the central hole is not very deep with respect to the bonding regions (ca. 15% density depression). Special emphasis has been given to the nature of the σ bonds forming the ring system. It has been found that the ring bonding in cyclopropane and in cyclopropene is due principally to three MO's: (1) A low lying MO (3a1) composed mainly of C(2s) AO's and contributing electron density principally inside the ring triangle. (2) Two MO's (6a1 and 3b2), which are the highest occupied MO's in cyclopropane and lie immediately below the π bond in cyclopropene, composed almost exclusively of C(2p) AO's in the ring plane and leading to electron density maxima outside the ring (density bending angle of ca. 20°) and to zero density in the centre of the ring. In the case of diazirine these MO's are appreciably perturbed by the presence of the nitrogen lone pairs. Three MO's contribute mainly to the description of the lone pairs, all of which also contribute to some extent to ring bonding. Furthermore, among these three MO's two lie below the π level, one of them being very low in energy. This is quite different from the usual picture. The present bonding picture has been compared to former semi-empirical models (especially the Coulson-Moffitt and the Walsh models). The strain, the “π” character and conjugative properties of the three-membered ring are discussed on the basis of its electronic structure. The special bonding features of this system confer on it a pseudo-π(ψ-π) character; the bonds making up the ring may be considered as ψ-π bonds.

Non empirical LCAO-MO-SCF calculations with gaussian type functions on some three membered ring heterocycles

Abstract: Non empirical molecular quantum chemical calculations have been performed on the three membered ring heterocyclic molecules, aziridine, oxirane and thiirane and the as yet unknown 1 azirene, 2 azirene, oxirene and thiirene. For the nitrogen compounds the corresponding protonated species have been investigated and for comparison the isoelectronic saturated and unsaturated hydrocarbon molecules, cyclopropane and cyclopropene. A discussion is given of total energies, eigenvalues, and gross atomic populations.

Calculs non empiriques sur une réaction SN2 typique

Abstract: On a calcule la structure electronique de l'etat initial et de l'etat de transition de la reaction de substitution F−+CH3F→FCH3+F− par la methode des orbitales moleculaires SCF dans l'approximation gaussienne. On trouve que l'energie de l'etat de transition est inferieure a la somme des energies des produits separes CH3F et F−. Cependant, cette contribution negative a l'energie d'activation est contrebalancee par la variation des energies de solvatation.

The geometries of molecular complexes: An extended Hückel approach

Abstract: The extended Huckel scheme of Hoffmann is approximated to allow relatively easy energy cal-calculations as a function of relative intermolecular geometry for a variety of planar charge transfer and charge resonance molecular complex pairs. The Hoffmann scheme is briefly discussed and the pertinent features of the method are illustrated with particular reference to weakly interacting molecular pairs. A dominant experimental structural feature is noted for all the complexes studied, in which a π-bond of one molecule is centered over and parallel to two edges of a hexagonal ring of the second molecule; it is basically a bonds-over-bonds arrangement. The calculated structures show good agreement with those observed for systems containing TCNE-like fragments and fair agreement for those in which this dominant structural feature occurs through the projection of two six-membered rings. In general no absolute binding is predicted. However, the agreement of relative minima between calculated and observed geometries coupled with the ease of calculation indicate the simple method may be useful in predicting relative geometries and further elucidating the more complicated structural features which must be involved.

The electronic structure of groups of isomeric hetero-aromatic systems: III. Hydroxy-pyridines and pyridones

Abstract: A discussion of the electronic structure of hydroxy-pyridines and pyridones shows that there is no reason for the point of view that the 3-oxo isomer, Β-pyridone, does not exist. N-methyl-3-pyridone was prepared and characterized to check this conclusion.The incorrect view is due to the assumption that the electron pairing scheme adopted in the valence bond method is necessarily implied in the classical formulae. This assumption should be replaced by a valence state interpretation of the classical symbols of atoms in molecules, independently of the method chosen for constructing the molecular wave-function.ZusammenfassungEine Diskussion der Elektronenstruktur von Hydroxy-Pyridinen und Pyridonen zeigt, da\\ es keinen Grund für die Annahme gibt, da\\ das 3-Oxo isomere Β-Pyridon nicht existiert. N-Methyl-3-Pyridon wurde hergestellt und untersucht, um diesen Schlu\\ zu prüfen. Der unkorrekte Standpunkt rührt von der Annahme her, da\\ das Elektronenpaar, welches der Valenzstrukturmethode zugrunde liegt, notwendigerweise in der klassischen Formel enthalten ist. Diese Annahme sollte durch eine Interpretation des Valenzzustandes der klassischen Symbole von Atomen in Molekülen ersetzt werden, unabhÄngig von der Methode, die zur Konstruktion der Molekülwellenfunktion gewÄhlt wird.RésuméLa discussion de la structure électronique des hydroxy-pyridines et des pyridones a montré qu'il n'y a pas lieu de supposer que l'isomère 3-oxo, ou Β-pyridone, n'existe pas. Cette conclusion a été confirmée par l'obtention et la caractérisation du N-methyl-3-pyridone.On a trouvé que cette opinion incorrecte est due à l'hypothèse suivante: le schéme de couplage électronique utilisé dans la méthode de la mesomerie (méthode V.B.) doit Être appliqué aux formules classiques. Cette hypothèse n'est pas necessaire et devrait Être remplacée par une interprétation des symboles classiques des atomes dans les molécules en fonction des états de valence atomiques, indépendamment de la méthode choisie pour la construction de la fonction d'onde moléculaire.

Semi-empirical molecular orbital calculations the electronic structure and the spin-orbit coupling in azabenzenes

Abstract: Electronic structures of pyridine, pyrazine, pyrimidine and pyridazine are studied by a semiempirical SCF method for valence electron systems previously proposed by the present authors. The charge distributions, transition energies and oscillator strengths of these compounds are calculated. The calculated results show fairly good agreement with the observed ones. Using these results, we have further calculated the oscillator strengths of singlet-triplet transitions \((f_{T_1 \to S_0 } )\) and the life times of the triplet states (τ). In this treatment, we have considered the mixing of various singlets with T1 and triplets with S0, and the effect of σ-electrons is studied.

GF calculation with minimal and extended basis sets for H2O, NH3, CH4 and H2O2

Abstract: A method is proposed for applying the theory of generalized group functions to SCF-GF calculations with large basis sets. A simple procedure for localising the SCF-MO's resulting from a standard SCF calculation is described, with applications to H2O, NH3, CH4 and H2O2. Results compare quite favourably with those obtained by the usual GF method. It is shown that when basis functions are the SCF-MO's and there are only two functions per group, the GF approach is practically equivalent to a configuration interaction treatment where only double excitations within the groups are considered.

Determination of molecular properties by the method of moments

Abstract: Basic principles of a possibility of simplifying the unrestricted spin-projected Hartree-Fock equations by means of the method of moments are outlined.

The electronic structure of boron trifluoride

Abstract: The electronic structure of boron trifluoride has been calculated ab initio by using extended basis sets of Gaussian type atomic orbitals. By variation of the B-F bond length a minimum energy situation was found at 1.306 a (experimental 1.31 a). Calculations on the pyramidal (reorganised) form of the molecule led to a reorganisation energy of 34.2 kcal mole−1. The π localisation energy was found to be 50.4 kcalmole−1. Both the latter energy and the π charge distribution are in good agreement with results from a previous Pariser-Parr-Pople calculation. The calculated quantities are used to discuss the energetics of donor-acceptor complex formation.

Electronic structure of high π-electron systems (graphite, polyacene, cumulene)

Abstract: The electronic structure of graphite, polyacene and cumulene are calculated by a generalised Hartree-Fock method, where electrons with different spins occupy different molecular Orbitals.

On a variational method for determining excited state wave functions

Abstract: A variational method is proposed which results in an approximate wave function for an excited state which has the maximum overlap with the true excited state eigenfunction. The method involves the calculation of the quantities E=〈Φ¦H¦Φ〉 and Δ=〈Φ¦(H-E)2¦Φ〉, but is free of the constraint that the trial function Φ must remain orthogonal to all states of the same symmetry which lie beneath it. One must know, however, an approximation to the true eigenvalue. A discussion is given on how one might gain the latter information, lacking knowledge of the spectrum, from the repeated application of the method.