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%.     

Quantum calculation of the intrinsic torsional barrier of C-C and C-O bonds

PCILO and ab initio calculations have been performed to investigate the energies associated to rotation about the central bond in n-butane and methyl ethyl ether. Quantum mechanical energies have been fit to a classical intramolecular force field, containing torsional and nonbonded (Lennard-Jones 6–12 plus Coulomb) contributions, with a standard deviation comprised between 0.03 and 0.09 kcal mol^–1. Two conditions have proved indispensable to reach such level of accuracy: (a) the use of a torsional potential with threefold periodicity, which corrects for the part of the rotation barrier not covered by van der Waals repulsions and may be interpreted as bond-bond repulsion; (b) the introduction in the force field for ethers of terms accounting for orbital interaction effects of different nature than the normal molecular mechanics nonbonded interactions; these terms are represented either by low order rotational potential functions or preferably by interactions of atoms simulating lone-pair orbitals and bonded to oxygen in such a way as to render it sp ³-hybridized. According to ab initio, the height of the threefold torsional potential about C-C and C-O bonds is comparable and is of the order of 3 kcal mol^–1. According to PCILO, it is larger for C-C (ca. 1.5 kcal mol^–1) than for C-O (ca. 0.5 kcal mol^–1).     

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 Electronic Interaction Energies Between Localized Orbitals

Localized molecular orbitals have been shown to be transferable among structurally-related molecules. We further show that the electronic energies between localized orbitals are transferable and their magnitude can be estimated. A set of parameters of group interaction energies are established from the analysis of small molecules. Use of these parameters is demonstrated successfully for large molecules.     

Application of intermolecular SCF-perturbation theory to the regioselectivity in the Diels-Alder reaction

Intermolecular perturbation theory in the density matrix formalism is applied to investigate the directional behaviour of an electron-donating (-CH₃) or an electron-accepting (-CN) group in 1- or 2-substituted butadienes in the Diels-Alder reaction with acrylonitrile. The calculated CNDO/2 perturbation energies are analysed in three different ways by considering: a) the different perturbation energies, b) the diatomic parts of the interaction energy and c) the HOMO-LUMO contribution to the second-order energy. The regioselectivity is due to a subtle balance of charge-transfer interactions and steric effects of the substituents on the diene and the dienophile. The changes of intra- and intermolecular diatomic energy contributions are correlated with the process of bond formation and bond weakening. The intermolecular perturbation energies are dominated by pairwise interactions between the terminal C-atoms and by the secondary Woodward-Hoffmann interaction. These three localized interactions determine the endo addition and reflect the orienting power of the substituents.     

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     

A theory of molecules in molecules IV. Application to the Hydrogen Bonding Interaction in NH3 · H2O

The theory of molecules in molecules introduced in previous articles is applied to study the hydrogen bonding interaction between an ammonia molecule as proton acceptor and a water molecule as proton donor. The localized orbitals which are assumed to be least affected by the formation of the hydrogen bond are transferred unaltered from calculations on the fragments NH₃ and H₂O, the remaining orbitals are recalculated. A projection operator is used to obtain orthogonality to the transferred orbitals. Additional approximations have been introduced in order to be able to save computational time. These approximations can be justified and are seen to lead to binding energies and bond lengths which are in satisfactory agreement with the SCF values. The point charge approximation for the calculation of the interaction energy between the two sets of transferred localized orbitals is, however, not applicable in this case. An energy analysis of the effect of the hydrogen bond on the localized orbitals of the two fragments is given.     

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.     

Note on the ab initio PUHF treatment of open-shell systems

Ab initio projected-unrestricted Hartree-Fock calculations have been carried out on a number of excited and ionic states of the water molecule. Results have been compared with large-scale CI calculations, with IVO calculations, and with those of Mrozek and Golebiewski obtained by the 2 × 2 rotation method applied to orbitals. It is concluded that the PUHF method may provide the most useful alternative to large-scale CI for calculating properties of open-shell systems. But it will not be generally useful for calculating spectral transition energies.     

The physical nature of the lone pair

Despite the large number of experimental and theoretical studies on the size, shape, and orientation of lone pairs and their resulting stereochemical character, lone pairs still remain poorly defined in terms of quantitative observable properties of a molecule. Using the conformation of saturated molecules and barriers to internal rotation, experimental chemists have arrived at conflicting sizes and orientations for lone pairs. Most theoretical attempts to define lone pair properties have centered on such non-observables as localized molecular orbitals or have been based on studies on isolated molecules.The use of observable properties to construct a consistent set of physical models to analyze the physical nature of lone pairs is discussed. Much as one probes an electric field with a test charge, probes such as H⁺, H^–, He and H could be used to probe regions of molecules such as NH₃ and H₂O where lone pairs are often postulated to exist.Ab initio quantum mechanical studies can be analyzed using electron density (and resulting changes during interaction), total pair density of electrons, the electrostatic potential about the molecule and bond energy analysis to study lone pair properties. A simple study of NH₃ using an H⁺ probe is presented to clarify the approach.     

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.     

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.     

Investigation of intermolecular interactions based on the atomic statistical model

Possibilities of improving individual contributions to the statistical interaction energy (kinetic and exchange) are examined. A new method of calculating statistical interaction energies is proposed. The exchange term is calculated using a suitably modified second-order gradient correction. For the kinetic contribution the accurate formula corresponding to the first-order perturbation theory is applied. The calculations have been carried out for several pairs of noble gas atoms.     

Conformational analysis of dimethylphosphate with quantum-mechanical and classical methods

In order to shed light on the conformational behavior of polynucleotide chains, and in particular to clarify the origins of the barriers to internal rotation in the phosphodiester linkage, we computed, with a quantum-mechanical ab initio procedure, the energies associated to 86 combinations of the two torsion angles in the dimethylphosphate anion (CH₃O)₂PO₂ ^–, and then we sought for an analytical expression apt to reproduce these energies with the highest possible accuracy. An excellent agreement (standard deviation of the fitted energies from the ab initio energies 0.28 kcal/mole) with the quantum-mechanical calculations was reached with a potential consisting of four terms: 1) a 6–12 Lennard-Jones contribution, in which different parameters are used to describe the interactions of methyls with the ester oxygens and with the anionic oxygens; 2) a contribution with twofold periodicity, accounting for the anomeric effects connected to the interactions between the lone pair electrons and the polar bonds of phosphorus with the anionic oxygens; 3) a contribution with threefold periodicity, representing the usual bond-staggering term; and 4) a Coulombic contribution, arising from electrostatic interactions between partially charged atoms.     

镱硫属化合物的密度泛函理论研究

用密度泛函理论(DFT)研究镱硫属化合物的电子结构和性质,通过与实验比较考察了现有的几种近似密度泛函公式对镧系元素化合物的适用程度和相对论效应的影响.结果表明,用DFT计算的YbO键长对实验值的偏差约为0.002nm;但得到的键能即使在考虑梯度校正和相对论效应之后,仍比实验值高,在定域密度近似基础上引入交换梯度校正使键能计算值减小,其中PW86x使键能计算值减小稍多些,结果更接近实验值;相关梯度校正使键能计算值升高.相对论效应使键长缩短0.004～0.006nm,键能减小约0.5eV.计算结果的分析表明,Yb的5d轨道和配体的np轨道间形成σ键和π键.在所研究的分子体系中,配体原子从O到Te、Yb原子的5d轨道布后数依次减少,同键能减弱的顺序一致.相对论效应使键能减小的主要原因是在成键过程中发生了Yb的6s电子向5d轨道的转移,而相对论效应使该过程能量增加.偶极矩和电荷分布的计算表明,Yb-L键以共价性为主,相对论效应使共价性成份增加.     

Coupling constants in the direct configuration interaction method

A general algorithm of evaluation of the coefficients of molecular integrals (coupling constants) appearing in the direct configuration interaction method is derived. The configurations are assumed to be spin-adapted antisymmetrized products of orthonormal orbitals. No limitation is imposed either upon the reference state (the number of the singly occupied orbitals may be arbitrary) or upon the excitation multiplicity.     

Electronic structure of monosubstituted benzenes and X-ray emission spectroscopy

The electronic structure of the benzaldehyde molecule has been studied by X-ray emission spectroscopy. The gas-phase O-K- and C-K-spectra of this compound have been obtained. MNDO quantum-chemical calculations have been carried out. The structure of the MO's of benzaldehyde has been compared with those of benzene and formaldehyde molecules. The character of the p-p interaction of the phenyl and formyl fragments has been considered. The contribution of the latter to the highest occupied molecular orbitals of the-system has been shown to be small.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1033–1037, June, 1994.