Transferability of some properties of localized molecular orbitals

The localized molecular orbitals of some related ten- and eighteen-electron systems have been studied. The transferability of the kinetic, self-interaction, Coulomb and exchange interaction energies on localized orbitals have been shown. The standard deviation of the kinetic and of the interaction energies (including exchange) are less than 2.5% except for lone pair orbitals of the oxygen atoms where the standard deviation is close to 4%.     

Delocalization corrections to the strictly localized molecular orbitals: A linearized SCF approximation

An explicit formula is derived for calculating the delocalization corrections (tails) to be added to the strictly localized bond orbitals. It was obtained by solving analytically the SCF problem for the interbond interactions in a linearized approximation. The model calculations at the CNDO/2 level show that this simple approach is sufficient to account for the molecular conformations.     

Application of the independent electron pair approach to the calculation of excitation energies,ionization potentials,and electron affinities of first row atoms

Excitation energies, first ionization potentials and electron affinities of first row atoms are calculated with a spin-adapted independent electron pair approximation (IEPA) combined with the direct determination of pair natural orbitals (PNOs). To enable comparison with molecular calculations Gaussian basis sets are used which are small enough to be also applicable to molecules. IEPA results for the above mentioned properties are accurate to 0.1–0.3 eV which is almost one order of magnitude better than the corresponding SCF-results. The same accuracy can be expected for molecules in which a localization of the doubly and singly occupied orbitals is possible, for instance for small hydrides. This is supported by the results of calculations on carbon hydrides.     

Bonding criteria for diatomic molecular orbitals and inter-relations among them

Bonding criteria for molecular orbitals in diatomic molecules are discussed. An orbital force criterion is shown to have several conceptual and practical advantages, providing a basis for the investigation of inter-relations among many of the commonly employed criteria.It is found that interconsistency among those criteria is guaranteed, within the framework of Koopmans' Theorem, if the orbital energies are monotonic in the range (R _e, ).The application of the orbital force criterion to the second row homonuclear diatomics exhibits reasonable chemical trends concerning the valence-shell orbitals, as well as indications of a slightly antibonding nature of the inner orbitals.Based on a section of a thesis to be submitted by Y.T. to the Senate of the Technion-Israel Institute of Technology, in partial fulfilment of the requirements for the D.Sc. degree     

Configuration interaction methods for improving unrestricted Hartree-Fock spin densities

Limited Configuration Interaction wave functions based on Unrestricted Hartree-Fock natural orbitals are found to be easy to compute and to give much more satisfactory spin densities than are provided by techniques currently in use.     

Basis set dependence of localized orbitals

The effects of Gaussian basis set contraction and addition of polarization functions on H₂O localized orbitals have been studied at the experimental geometry. It is shown that the electric moments and moment features of localized orbitals are not influenced very much by basis set quality variations, as going from medium size to enlarged basis sets. The difference between bond pair and lone pair charge densities was found to be larger on approaching the Hartree-Fock limit. A minimal basis set, however, does not suitably characterize the localized charge distributions.     

Transferability of some properties of localized molecular orbitals

The transferability of the first and second order electric moments of localized orbitals have been shown. Some moment characteristics have also been investigated. The standard deviation of first order localized moments is less than 2.0%. The standard deviation of second order electric moment components are larger: although they do not exceed 4.0% for bond orbitals, for lone pair ones they vary about 1.5–10.1%.     

Discrete Variational (DV)-Xα Calculations of Incomplete Cubane-Type Molybdenum Clusters [Mo3X4(H2O)9]4+ (X= O,S)1

Electronic structures of two incomplete cubane-type clusters [Mo₃X₄(H₂O)₉]⁴⁺ (X =O, S) have been calculated by the discrete-variational (DV)-X method. The calculations explain the experimental results of valence-band X-ray photoelectron spectra, electronic spectra, and reactivity difference toward acetylene. The net charge of Mo in [Mo₃S₄(H_2O)₉]⁴⁺(S) is more negative than that of Mo in [MO₃O₄H₂O)⁴⁺] (O), and the bridging sulfur atoms are the main negative charge-source for the molybdenum atoms in the cluster S. As for S,levels of HOMO (45e) and LUMO (46e) consist mainly of Mo 4d and-S 3p atomic orbitals, and contribution of ₃-S 3p to the orbitals is not large. The existence of Mo-Mo, Mo--S, and Mo- ₃-S bounds is clear from the contour maps of the orbitals. As for O levels of HOMO (40e) and LUMO (41c) consist mainly of Mo 4d and-O 2p atomic orbitals. Contribution of ₃-O 2p to the orbitals is not large except in the orbital 30a₁,. The existence of Mo-Mo, Mo--O, and MO- ₃-O bonds also is appreciable from the contour maps of the orbitals.Dedicated to Professor Jiaxi Lu on the occasion of his 80th birthday.     

Band structure of nonclassical polymers

It is shown that fully conjugated alternant nonclassical polymers are comparatively stable systems as a result of the considerable delocalisation energy.The energy characteristics of the polymers are strongly determined by the electron spin distribution of the degenerate nonbonding molecular orbitals; the full spin configuration,S>0, is favoured. The spin densities depend on the electron correlation and alternate; this corresponds to a ferrimagnetic state of the polymer at 0°K.     

Eletronic structure of monosubstituted benzenes and X-ray emission spectroscopy

The electronic structure of benzonitrile has been studied by X-ray spectroscopy. N-K and C-K spectra were recorded. The corresponding theoretical spectra were constructed on the basis of MNDO calculations. The molecular orbitals (MO) of benzonitrile have been compared with those of benzene and hydrogen cyanide. The p-p-interaction between the phenyl fragment and the cyano group has been studied. The contribution of the latter to the highest occupied orbitals of the molecule was shown to be small.For part 1, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1251–1254, July, 1994.In conclusion, the authors would like to thank Prof. D. S. Werch (Queen Mary College, London) who put the OHM crystals at their disposal.     

Calculation of polarizabilities by the CNDO method

The polarizabilities of a number of small and medium size molecules are calculated using CNDO/2 wave functions. The first-order and the second-order perturbation equations are solved by variational procedures. The results are encouraging for the component along the internuclear axes and in the molecular plane. The effect of deorthogonalization of the CNDO/2 orbitals is discussed.     

Evaluation of fourier transform of two-center charge distribution for arbitrary slater-type orbitals

Fourier transform of two-center charge distributions corresponding to arbitrary Slater-type orbitals are evaluated by a Gaussian quadrature procedure without any preliminary series expansion of the integrand. Convergence and accuracy of the method are discussed and illustrated.     

Iterative natural orbitals for configuration interaction using perturbation theory

Approximate natural orbitals are determined iteratively from CI expansions constructed using first-order perturbation theory in order to investigate the possibility of eliminating the complete transformation of MO integrals on each iteration. Results on LiH and H₂O are compared with fully variationally determined NO's to assess questions of convergence.     

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.     

Molecular orbital calculations based on linear combinations of fragment orbitals

A semiempirical MO method based on localized fragment orbitals has been developed, which is particularly suited for the construction of orbital correlation diagrams for the discussion of the electronic structure of complex molecules in terms of fragments and their interactions. The method allows for the inclusion of experimental ionization potentials and electron affinities of the fragments within the calculation of the Fock matrix elements and may thus form the basis of an interpretation of photoelectron spectra, comparable to the interpretation of UV spectra by means of the MIM method of Longuet-Higgins and Murrell. Several levels of approximation are discussed using the acrolein molecule as an example.     

A theory of molecules in molecules

A theory of molecules in molecules is presented, which permits the computation of the wave function of a molecule from the wave functions of fragment molecules by transferring some of the localized molecular orbitals of the fragments and recalculating the orbitals in the region of interaction. A projection operator is used to obtain orthogonality of the orbitals to be determined to the transferred and fixed orbitals. Additional approximations allow the reduction of the dimension of the matrices to be diagonalized and the neglect of a part of the basic integrals, which can lead to a considerable saving in the computation time. The justification of these approximations will be investigated for the case of the molecules Be-Be, Li₂-Li₂, and for the calculation of the rotational barrier in C₂H₆.     

The electronic spectra of the alkyl,fluorine and chlorine substituted derivatives of silane

The main characteristics of the ultraviolet absorption spectra of simple alkyl, fluorine and chlorine derivatives of silane are described. The interpretation of these spectra is discussed in relation to the respective photoelectron spectra, the Rydberg-valence-shell distinction and involvement of 3d atomic orbitals.Dedicated to Professor Dr. Hermann Hartmann on the occasion of his 65th birthday.     

The evaluation of ω parameters in contracted density product calculations

General formulas for the rotational averages of two electron integrals with arbitrary combinations of spherical tensors in standard, Cartesian, and equivalent form are presented. The way in which the parameters of CDP type calculations can be obtained from rotational averages is discussed, and it is shown from numerical results that the interpretation of the parameters as space averages is compatible up to d orbitals with the CDP invariance requirements.     

Inclusion of dynamic σ-π polarization in π-electronab initio calculations

Summary A method is presented, whereby dynamic - polarization, i.e. the correlation effect expressed by simultaneous (-*, -*) excitations, can be approximately included in a multi-reference configuration interaction (MRCI) or multi-configurational self-consistent field (MC-SCF) calculation, without need to explicitly correlate the sigma orbitals. The method, which we call the capacitance matrix method, is based on the use of conventional one-electron integrals, from which a polarization potential (SPP) contribution is computed and added to the one- and two-electron Hamiltonian. In the present form, the method requires one parameter for each type of atom, and one for each type of bond. These parameters were adjusted to reproduce the dynamic - polarization energy, computed by restricted multi-reference CI calculations, of a number of states of different hydrocarbons, and the agreement was within a few percent. Using the same parameters in CAS (Complete Active Space) SCF calculations of various states of benzene gives excitation energies, when SPP is included, which is comparable to those obtained by much more elaborate MRCI calculations.