Anisotropy of diamagnetic susceptibility of alternant hydrocarbons

The anisotropy of diamagnetic susceptibility of several hydrocarbons has been calculated with the use of the SC LCAO MO method with the London theory. The results for 10 hydrocarbons are compared with experiment and other known theoretical approaches. It is found that the SC LCAO MO method leads to a best agreement with experiment.

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Zusammenfassung Die Anisotropie der diamagnetischen Suszeptibilität mehrerer Kohlenwasserstoffe wurde im Rahmen der Londonschen Theorie nach der SC LCAO MO-Methode berechnet. Für 10 Aromaten werden die Ergebnisse mit dem Experiment und anderweitig berechneten Werten verglichen. Die SC LCAO MO-Resultate zeigen die beste Übereinstimmung mit dem Experiment.

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Résumé L'anisotropie de la susceptibilité diamagnétique de plurieurs hydrocarbures a été calculée par la méthode SC LCAO dans le cadre de la théorie de London. Pour 10 hydrocarbures on compare les résultats à l'expérience et aux résultats d'autres théories. La méthode SC LCAO MO rend le meilleur accord avec l'expérience.

     

Partial LCAO densities of states for ScN,TiN, ZrN and ScP

Densities of states (DOS) and partial densities of states were calculated from self-consistent APW band structure calculations for four transition metal compounds (ScN, TiN, ZrN and ScP) using a recently published improved LCAO interpolation scheme. The total DOS and the LCAO non local partial metal s, p and d and non-metal s and p DOS of these compounds are presented and compared with non local LCAO partial DOS from earlier calculations as well as with local partial DOS obtained directly from the APW or LAPW wave functions. A LCAO charge analysis for all valence states and for the individual valence bands is also given.     

Maximum overlap symmetry orbitals

Based on the principle of maximum overlap, a new simple method is suggested for constructing the symmetry orbitals of arbitrary molecules and the delocalized molecular orbitals of molecules that do not involve the rings with an odd number of atoms. All these orbitals, called “maximum overlap symmetry orbitals,” are determined by an extended maximum overlap criterion and form the bases for the irreducible representations of the molecular point symmetry group. The theoretical analysis and the numerical results show that the obtained molecular orbitals are close to those obtained from the customary LCAO method, and calculation by the proposed method requires less computing time than does the LCAO method, thus illustrating a fact that the method is not only a reasonable approximation of the LCAO method, but simpler and feasible in large molecular systems.     

Relativistic density functional calculations using two-spinor minimax finite-element method and linear combination of atomic orbitals for ZnO, CdO, HgO, UubO and Cu2, Ag2, Au2, Rg2

In previous work the authors have presented a highly accurate two-spinor fully relativistic solution of the two-center Coulomb problem utilizing the finite-element method (FEM) and furthermore developed a relativistic minimax two-spinor linear combination of atomic orbitals (LCAO). In the present paper the authors present Dirac-Fock-Slater (DFS-) density functional calculations for two-atomic molecules up to super heavy systems using the fully nonlinear minimax FEM and the minimax LCAO in its linearized approximation (linear approximation to relativistic minimax). The FEM gives highly accurate benchmark results for the DFS functional. Especially considering molecules with up to super heavy atoms such as UubO and Rg2, the authors found that LCAO fails to give the correct systematic trends. The accurate FEM results shed a new light on the quality of the DFS-density functional.     

He2+2: A comparison between Hartree–Fock and density functional techniques

A comparison of Roothaan-Hartree–Fock methods (both restricted and unrestricted) with density functional ones (LCAO -Xα and cellular MS -Xαβ) is made using as test case the He²₂ + molecular ion. It is shown the analogy that exists between RHF and symmetry-adapted LCAO -Xα potential energy curves, as well as between UHF and symmetry-unconstrained LCAO -Xα ones. The influence of symmetry adaptation on the overall behavior of the potential energy curve is also discussed. Finally, the difference in the behavior of the LCAO -Xα and cellular MS -Xαβ calculations is explained as an artifact of the space partitioning in the latter technique. It is concluded that LCAO -Xα method is superior to cellular MS -Xαβ because it requires less effort to reach the same results and that the general behavior is similar to UHF , although the former affords a better equilibrium bond distance and a worse energy barrier than the latter.     

Computation of LCAO wave functions for ground states of polymers and solids

The LCAO form of the Hartree–Fock method is discussed in its application to crystals. General formulae are given for obtaining Fourier coefficient of electronic density (in direct space) as well as of the band structure (in momentum space). Finally, it is shown that in its LCAO form, Slater–Hartree–Fock equations are very simple and that this method is of interest for numerical applications. Special integrals occurring in this formalism are evaluated for a Gaussian basis in the last part of this paper.     

Calculation of the tetraphenylcyclobutadiene molecule by the MO LCAO method

Summary From the point of view of the simple MO LCAO method, there are no grounds for supposing that the tetraphenylcyclobutadiene molecule would be stable.     

Wannier-type atomic orbitals for periodic systems

The results of an application of Wannier-type atomic orbitals for calculations of local properties of electronic structure for periodic systems (atomic charges and covalencies, bond orders and total valencies), published earlier by the authors, are summarized. The numerical results are given for bulk crystals with the perovskite structure ATiO₃, A=Sr,Ba,Pb and LaMnO₃ (the Bloch functions are calculated in LCAO basis), for bulk MgO crystal (the Bloch functions are calculated both in LCAO and PW basis) and for the two periodic slab models of surfaces (001) of MgO and (110) of rutile TiO₂.     

Combined SSF MO LCAO and correlation density functional method applied to adsorption of atomic hydrogen on lithium clusters

An SSF MO LCAO + CDF Method is developed, in which supplementary to a nonempirical SSF MO LCAO calculation the correlation energy of a many electron system is estimated as a functional of the electron density E_C[]. To check the effectiveness of this procedure for calculating the E_C[] functional, E_C is calculated for monohydrides of elements in the second and third columns of the periodic table. The SSF MO LCAO + CDF is applied to a comparative calculation of the adsorption of atomic hydrogen on lithium clusters with different multiplicity and the role of the electron correlation in this process is established.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 4, pp. 385–392, July–August, 1989.     

Hückel and möbius boundary conditions for solids and orbital symmmetry correlation in the rotational phase transition of molecular crystals

A new cyclic boundary condition which corresponds to a Möbius strip representation of a one-dimensional crystal is introduced. It is compared with the usual Bloch and Born—von Karman boundary condition which is shown to be a Hückel condition in the sense of LCAO MO treatment of a ring structure. The potential relevance of this Möbius condition to one-dimensional molecular and liquid crystals in which the relative molecular orientation changes during phase transition is alluded to. A comparison of the energies for the twisted and non-twisted form of the linear crystal is derived in the LCAO approximation. The orbital symmetry correlation in the concerted twist of the atomic or molecular orbitals atom! the linear backbone during a rotational polymorphic structural transition is also derived.     

A remark on doublet stability of allyl radical restricted SCF solutions

The doublet stability of ab-initio SCF LCAO solutions for the allyl radical is re-examined for a wide range of CC bond lengths with the minimum, double zeta and double zeta plus polarization atomic orbital basis sets.     

Basis set considerations for the calculation of gradients in the lcao formalism

Compact expressions are derived for the analytical gradient with a general MC SCF LCAO wavefunction. Cancellations among the terms involved are shown to have important computational aspects, and substantial reductions of computer time may be achieved with a properly chosen basis set.     

Theoretical study of isoelectronic systems: Diazomethane,ketene and allene

All-electron SCF –LCAO –MO computations for diazomethane, ketene and allene are presented. The basis functions are contracted Gaussian orbitals. Theoretical results are discussed and related to available experimental data.     

CI treatment of charged TCNQ clusters in a localized basis: Connection with the extended Hubbard model

A procedure has been developed which makes it possible to transform delocalized SCF LCAO molecular orbitals of charged TCNQ clusters (normalized neglecting overlap) into the localized molecular orbitals having the character of slightly perturbed SCF LCAO monomer orbitals. It has enabled us to formulate the conventional CI hamiltonian in the localized basis and to estimate the interaction parameters. It has been found that the transformed CI hamiltonian may be replaced by the extended-Hubbard-model hamiltonian with high accuracy. The estimated strength of the Coulomb interactions between unpaired electrons has been found to be much greater than the typical electronic bandwidth of TCNQ sats or complexes.     

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.     

LCAO–MO similarity measures and taxonomy

Similarity measures between pairs of molecular wave functions are described. They are based on the geometrical structure of the LCAO–MO framework and upon multivariate analysis ideas. The theoretical framework is presented, and formulae for some integrals needed are given. Two main measures, distance and correlation coefficients, are used. Distance and correlation matrices induce relationships in the whole MO set, which can be depicted through minimal spanning tree techniques. Furthermore, principal component analysis allows a two-dimensional visualization of the Mo manifold geometrical relationships. Various examples are given in order to obtain information on how basis set, environment, excitation, bending, stretching, and electronegativity affect the induced order. For this purpose “ab initio” SCF–LCAO–MO calculations with double- and single-zeta quality basis sets have been used for various simple molecular structures: H₂O, NH₃, CH₄, N₂, O₂, C₂, NO, CN, and CO. The results obtained can open the way to LCAO–MO taxonomy. Using this information, other areas of interest are connected with similarity measures (SCF and CI , localization procedures, etc.), proving in this manner their potential utility.     

Relativistic symmetry orbitals for the double groups C2v,C∞v,D∞h,and Oh

Relativistic symmetry orbitals are given for molecular LCAO calculations for the double groups: C_2v, C_∞v, D_∞h, and O_h (6-fold) coordination. The atomic orbitals used in the LCAO are of the four component form. A discussion of the comparison between nonre ativistic and relativistic molecular eigenvalues is presented.     

Novel sign-alternation rule for the triplet state in aromatic systems

Within the framework of the LCAO -MO theory, a novel sign-alternation rule has been found empirically for the lowest excited ππ* triplet state in the alternant aromatic system. This rule can be applied to identify the phosphorescent state.     

Magnetic properties of conjugated molecules

An LCAO SCF perturbation theory is used to discuss the diamagnetic susceptibility and shielding constant contributions associated with ring currents in aromatic molecules. The proton shielding constants are calculated directly from the current density expression for benzene, naphthalene, anthracene and phenanthrene.