On the asymptotic behavior of Hartree-Fock orbitals

Summary Handy et al. have shown that the asymptotic behavior of Hartree-Fock orbitals is controlled by the energy of highest occupied molecular orbital, except for the atomic case in which onlys-orbitals are occupied. However, their proof is not complete at one point. This point is clarified, and a more unified derivation is given. Further, we discuss the preexponential factorr of the leading asymptotic termr exp[–r], where =(–2_HOMO)^1/2 and _HOMO is the orbital energy of HOMO. New results are obtained for linear molecules, and the results of several authors for atoms and non-linear molecules are reproduced.     

Ab initio calculation of maximum bond order hybrid orbitals

Summary The maximum bond order hybrid orbital (MBOHO) procedure is tested onab initio level by use of the density matrix in Löwdin orthogonalized atomic orbital basis. The direct MBOHO calculation based on the whole density matrix includes also the hybridization of the inner atomic orbitals, and the MBOHO calculation based on the valence orbital part of the density matrix considers only the hybridization of the valence atomic orbitals. The concrete MBOHO calculations based on theab initio calculation with STO-3G basis show that the components of the s atomic orbitals in MBOHOs and the maximum bond orders obtained from the two kinds of MBOHO calculations are very close to each other, and that the two kinds of MBOHOs all have the excellent correlativity with the nuclear spin-spin coupling constants.The project supported by National Natural Science Foundation of China and the Excellent Young University Teacher's Foundation of State Education Commission of China.     

Some remarks on the maximum bond order

Summary Some remarks are given concerning the recent improvement scheme of calculating Jug's maximum bond border index.     

General properties of the hartree-fock problem demonstrated on the frontier orbital model

The general Hartree-Fock energy in the frontier orbital model in the terms of independent variables is given. The existence conditions for extrema of this expression are derived and their relation with various types of solutions of the HF problem as RHF, UHF and complex wavefunctions is shown. The connection between overall properties of the energy surface and the local properties i.e. the stability and instability conditions of various kinds is demonstrated. The conditions for the occurrence of strange HF solutions are expressed in terms of quantities characterizing the correlation effects. This shows explicitly that the lack of respecting the electronic correlation is the reason for the occurrence of the strange HF solutions for the molecular configurations which exhibit a certain amount of diradical character.The summary of the results has been presented at the 6th Jerusalem Symposium on Quantum Chemistry and Biochemistry and at the I. Congress of Quantum Chemistry, Menton, July 1973.On leave of absence from Institute Rudjer Bokovi, Zagreb, Yugoslavia.     

Classical structures in modern valence bond theory

The results of some recent ab initio valence bond calculations, in which both structure coefficients and orbital forms are optimized, are analysed. The origin of structures in which the optimum orbitals are no longer atomic in character but instead delocalized, is traced back to the presence of certain symmetries in the wavefunction. When such symmetries exist it is possible to choose alternative linear combinations of the delocalized orbitals and to rewrite the wavefunction in terms of VB structures of classical form. The advantages of the classical structures are discussed in the context of a simple example — a square planar conformation of four hydrogen atoms.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Comparison of the Bonding of Benzene and C60 to a Metal Cluster: Ru3(CO)9(μ3-η2,η 2,η2-C6H6) and Ru3(CO)9(μ3-η2,η2,η2-C60)

The electron distributions and bonding in Ru₃(CO)₉( ³- ², ², ²-C₆H₆) and Ru₃(CO)₉( ³- ², ², ²-C₆₀) are examined via electronic structure calculations in order to compare the nature of ligation of benzene and buckminsterfullerene to the common Ru₃(CO)₉ inorganic cluster. A fragment orbital approach, which is aided by the relatively high symmetry that these molecules possess, reveals important features of the electronic structures of these two systems. Reported crystal structures show that both benzene and C₆₀ are geometrically distorted when bound to the metal cluster fragment, and our ab initio calculations indicate that the energies of these distortions are similar. The experimental Ru–C_fullerene bond lengths are shorter than the corresponding Ru–C_benzene distances and the Ru–Ru bond lengths are longer in the fullerene-bound cluster than for the benzene-ligated cluster. Also, the carbonyl stretching frequencies are slightly higher for Ru₃(CO)₉( ³- ², ², ²-C₆₀) than for Ru₃(CO)₉( ³- ², ², ²-C₆H₆). As a whole, these observations suggest that electron density is being pulled away from the metal centers and CO ligands to form stronger Ru–C_fullerene than Ru–C_benzene bonds. Fenske-Hall molecular orbital calculations show that an important interaction is donation of electron density in the metal–metal bonds to empty orbitals of C₆₀ and C₆H₆. Bonds to the metal cluster that result from this interaction are the second highest occupied orbitals of both systems. A larger amount of density is donated to C₆₀ than to C₆H₆, thus accounting for the longer metal–metal bonds in the fullerene-bound cluster. The principal metal–arene bonding modes are the same in both systems, but the more band-like electronic structure of the fullerene (i.e., the greater number density of donor and acceptor orbitals in a given energy region) as compared to C₆H₆ permits a greater degree of electron flow and stronger bonding between the Ru₃(CO)₉ and C₆₀ fragments. Of significance to the reduction chemistry of M₃(CO)₉( ³- ², ², ²-C₆₀) molecules, the HOMO is largely localized on the metal–carbonyl fragment and the LUMO is largely localized on the C₆₀ portion of the molecule. The localized C₆₀ character of the LUMO is consistent with the similarity of the first two reductions of this class of molecules to the first two reductions of free C₆₀. The set of orbitals above the LUMO shows partial delocalization (in an antibonding sense) to the metal fragment, thus accounting for the relative ease of the third reduction of this class of molecules compared to the third reduction of free C₆₀.     

Freie Elektronenpaare in lokalisierten CNDO/2-Wellenfunktionen der Stickstoffverbindungen

The method for constructing hybrid orbitals described earlier is now used for the analysis of CNDO/2 wave functions of molecules containing nitrogen atoms in order to get information on the type of hybridization of nitrogen lone pair orbitals in various compounds.     

Selective Thermolysis of Azide Groups in 2,4,6-Triazidopyridines

When refluxed in 1,4-dichlorobenzene, the compound 2,4,6-triazido-3,5-dichloropyridine and its 3,5-dicyano derivative undergo selective thermolysis of the -azide groups, forming the corresponding 4-amino-2,6-diazidopyridines in high yields. According to quantum-chemical calculations, the selectivity of thermolysis of the -azide groups in triazides is due to the weaker bonding interactions between the N₍₎ and N₍₎ atoms in these azide groups.     

A quantified resonance theory and its relation with MO — excited state behaviour of conjugated hydrocarbons and heteroconjugate molecules

Summary Quantified resonance theory (QRT) involving the use of weight has been applied successfully to ionization potential, electron affinity, energy of the lowest * transition, charge density and bond order in excited state for alternant and nonalternant hydrocarbons and heteroconjugate molecules. A number of close relations between QRT and HMO or PMO are found. QRT naturally leads to the frontier orbital theory results, and the natural hypsochromic shift in electronic spectra of fulvenes is also explained satisfactorily.     

A concise representation of adsorbate-surface interactions. II. An application to Pt(111) + Co,W(110) + Co and Pt(112) + Co systems

A method is presented to represent the chemisorptive interactions concisely. The canonical molecular orbitals of a chemisorption system are transformed into new orbitals where the charge transfer interactions between the surface and the adsorbate are maximized or minimized. The chemisorptive bonds are well described by a small number of the transformed orbitals. The analysis of chemisorptive interactions is carried out for the Pt(111) + CO, W(110) + CO and Pt(112) + CO systems. The weakening of the C-O bond in the W(110) face and in the trench region of the Pt(112) face is larger than that in the Pt(111) face in conformity with the experimental data. The interactions are, to a good approximation, represented by five or six orbitals and are explained in terms of the and donation of CO to the surface and the back donation to CO.     

35Cl NQR Studies of the Geometry of Aromatic Imines

The preferred conformation of solidphase R4benzylidene3,4dichloroaniline molecules has been established by nuclear quadrupole resonance (NQR) combined with quantum chemical calculations. The conformational effect of substitutes reported previously is proved. The rotation angle of the plane of the aniline ring with respect to the plane of the azomethine bond is given.     

The calculation of valence angles for H2O and NH3 using the maximum overlap principle

A new approximate method for the determination of the valence bond angles for MX **** _k -type molecules, based on the maximum overlap principle, is proposed. The valence bond angles are determined from the conditions of maxima of the total bonds strength. The method has been used to calculate the valence angles and the hybrid orbitals for the water, and the ammonia molecule, respectively. The calculated valence bond angles for both molecules are about 2 too high with respect to experimental equilibrium values. Also the best hybrid orbitals using the Golebiewski simplified method were calculated.

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Zusammenfassung Eine neue NÄherungsmethode für die Bestimmung der Valenzwinkel für Moleküle vom Typ MX **** _k wird vorgeschlagen, die sich auf das Prinzip der maximalen überlappung gründet. Die Valenzwinkel werden aus der Forderung nach einem Maximum der GesamtbindungsstÄrke abgeleitet. Die Methode wird zur Berechnung der Valenzwinkel und der Hybridorbitale von H₂O und NH₃ angewendet. Die berechneten Valenzwinkel sind für beide Moleküle etwa 2 zu hoch gegenüber den experimentellen Gleichgewichtswerten. Die besten Hybridorbitale werden entsprechend der vereinfachten Methode von Golebiewski berechnet.

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Résumé On propose, sur la base du principe du recouvrement maximum, une nouvelle méthode approchée pour la détermination des angles des liaisons de valence des molécules de type MX **** _k . Ces angles sont déterminés à partir des conditions de maxima de la «force totale de liaison». La méthode a été utilisée pour calculer les angles de valence et les orbitales hybrides de l'eau et de l'ammoniac. Les valeurs obtenues sont supérieures d'environ 2 aux valeurs expérimentales. Les meilleures orbitales hybrides de ces deux molécules ont été aussi calculées par la méthode simplifiée de Golebiewski.

     

IR-Spectroscopic Study of the Binding Isomerism of Adsorbed Molecules

This paper discusses the use of IR spectroscopy in the studies of isomerism in the binding of adsorbed molecules with a surface when a molecule may form several different surface species at the same site. Species whose geometry does not provide minimal adsorption energy can be considered as adsorption complexes in an excited state. The spectral manifestations of such a steric excitation are compared with the electronic and vibrational excitations of surface species. The sterically excited isomeric states existing in thermodynamic equilibrium with ordinary adsorption species are found and studied in detail. Examples are CO molecules bound through C and O atoms with metal cations in zeolites or with surface hydroxyl groups, the thiophene molecule via hydrogen bonding with silanol groups, and HD molecules dissociatively adsorbed on ZnO. A possible role of sterically activated isomeric states in catalysis is discussed.     

MBOHO calculations of phosphorus-carbon nuclear spin-spin coupling constants

Summary The novel generalized correlation of the nuclear spin-spin coupling constants with the atomic hybrids and net charges is employed to give a new relationship for calculating the directly bonded phosphorus-carbon coupling constants by use of the maximum bond order hybrid orbital procedure together with the extended Hückel molecular orbital calculation. The calculated coupling constants of phosphorus-carbon are all in good agreement with the experimental data, which shows that the new relationship obtained in the present paper is quite satisfactory for calculation of the phosphorus-carbon coupling constants.The project was supported by the National Natural Science Foundation of China and the Excellent University Teacher's Foundation of State Education Commission of China     

Nuclear repulsion effects in molecular bonding

Potential energy curves of a single electron moving in the joint Coulomb field of two fixed nuclei of equal arbitrary charge, Z, have been calculated exactly using a scaling relationship derived in an earlier paper. The resulting potential curves display some interesting features. For Z<1 the 2p antibonding orbital becomes bonding, while the 1s potential well becomes deeper. For larger Z, the 1s orbital eventually becomes antibonding but the potential curve passes through a number of distinct intermediate stages before a purely repulsive potential is reached.     

Molecular integrals in the approximate calculation of electronic structure

A self-consistent set of new proposals is made for the calculation of the largest molecular integrals over orthogonal hybrid orbitals used in neglect of differential overlap schemes.     

Intramolecular Interactions in Anisole,Thioanisole, and Selenoanisole. Application of Natural Bond Orbitals Method

Calculations of molecules PhXMe (X = O, S, Se) in MP2(f)/6-31G(d) approximation were performed. The stationary points on the potential energy surface were determined and identified. The anisole molecule is planar with a barrier to rotation H 7.78 kJ mol^-1. In thioanisole and selenoanisole (H 3.08 and 10.25 kJ mol^-1 respectively) the energy minimum corresponds to an orthogonal form. Analysis of relation between intramolecular interactions and conformational structure of the molecules in question was performed by the method of natural bond orbitals. In X atoms one lone electron pair is a hybrid orbital with the following fraction of s-component: 38-45% (O), 66-68% (S), and 73-74% (Se). The second lone electron pair is virtually pure pz-AO.     

The resolution of some chiral compounds in reversed-phase high-performance liquid chromatography by means of β-cyclodextrin inclusion complexes

Summary -Cyclodextrin is applied as the chiral component of the mobile phase in a systematic study of the resolution —into enantiomers — of mandelic acid and its derivatives by reversed-phase liquid chromatography. It is found that the stereoselectivity arising from inclusion in -cyclodextrin molecules is significant (=1.02÷1.05) only for the compounds showing at the asymmetric carbon atom the presence of first, an intact carboxylic group and second, a functional group capable of hydrogen bonding with the hydroxyl groups of -cyclodextrin. Results are discussed in the light of the three-point attachment model of stereoselectivity as well as of the structure of the inclusion complexes.Presented at the 14th International Symposium on Chromatography London, September, 1982     

On the mathematical formulation and interpretation of LACO MO theory

The mathematical basis of LCAO MO theory is studied, both within the Hartree-Fock approximation and in more exact formulations. The basic LCAO expansion for molecular orbitals ¦> in terms of atomic orbitals ¦x> is conveniently written ¦> = ¦x> S ^–1 B where S is the overlap matrix for atomic orbitals and B is the matrix of atomic orbital-molecular orbital overlaps. It is suggested that matrices P and Q, defined by P=B B and Q=BnB where n is the matrix of molecular orbital occupation numbers, are appropriate to the interpretation of molecular calculations in terms of atomic orbital components, electronic populations and the degree of bonding. Implications for Hartree-Fock calculations are investigated.