Valency. II. Applications to molecules with first-row atoms

A quantum chemical definition of valency proposed in Part I is used to calculate the valency of carbon, nitrogen, oxygen, lithium, beryllium and boron in a number of compounds with the SINDO1 method. It is demonstrated that consistency of the basis set is necessary for comparable results. The general features of valency and bonding in these molecules are discussed. The π-electron concept of free valence is generalised to sigma systems and atoms in molecules are classified as subvalent, normal or hypervalent. The relation between valency and natural hybrid occupancy is illustrated. The symmetry properties of natural hybrid orbitals are discussed by means of group theory. A preliminary attempt is made to relate covalency and covalent reactivity. Bond indices and the σ, π character of bonds are obtained by a suitable partitioning and projection of valency into bonding and antibonding contributions. Alexander von Humboldt Fellow 1982–83.     

Calculation of the nonlinear optical properties of molecules

A finite-field method for the calculation of polarizabilities and hyperpolarizabilities is developed based on both an energy expansion and a dipole moment expansion. This procedure is implemented in the MOPAC semiempirical program. Values and components of the dipole moment (μ), polarizability (α), first hyperpolarizability (β), and second hyperpolarizability (γ) are calculated as an extension of the usual MOPAC run. Applications to benzene and substituted benzenes are shown as test cases utilizing both MNDO and AM1 Hamiltonians.     

Decoupled Hartree-Fock methods. II. Calculation of the potential curves of diatomic molecules

Applying an extended form of the Mulliken approximation and a monopole approximation for the Coulomb integrals the Hartree-Fock nonorthogonal energy expression is decoupled. Thus, the total energy splits into a sum of one-electron increments. The increments are minimized directly with respect to the linear coefficients and orbital exponents. Further, the ZDO approximation is used in the decoupled energy expression to avoid difficulties arising in connection with the evaluation of multicenter integrals. “Rigid core” calculations were carried out for the valence electrons of first-row diatomics. In case of nonpolar molecules good results are obtained for equilibrium distances and force constants. The method fails for molecules with atoms having very different nuclear charges.     

Properties of atoms in molecules

Atomic charges calculated by the population analysis method for three types of semi-empirical wave functions have been compared with charges obtained by integrating the corresponding electronic density functions over individual atomic regions. It was found that the two sets of charges compare quite well for CNDO wave functions and for extended-Hückel functions which are in terms of orthogonalized basis orbitals. However only the CNDO charges are reasonably close to those obtained by integrating near-Hartree-Fock electronic density functions.     

Properties of atoms in molecules

The electronic charges and the positions of the centers of these charges have been calculated for the atoms of a number of second- and third-row heteronuclear diatomic molecules. For both the oxygen and the fluorine atoms, the charge associated with one of these atoms can be correlated, within a series of molecules containing that atom, with both the orbital energy of the atom's 1s electrons and also with the difference in electronegativities of the atoms that comprise the molecule. The centers of electronic charge are outside of the internuclear regions, except for the positive atoms in the more ionic molecules and in HF.     

Ensemble-representable densities for atoms and molecules. II. Application to CoCl4 2−

In the previous article we introduced a method to obtain an ensemble density describing a molecule in a crystal from diffraction experiment structure factors. Here the method is applied to the CoCl₄²⁻ molecular ion in a Cs₃CoCl₅ crystal for which accurate magnetic structure factors are known. First, the approximations involved in the interpretation of polarized neutron experiment are reviewed with special emphasis on the collinearity approximation which has been avoided in this work. Second, the derivation of magnetic structure factors corresponding to theoretical ensemble densities is explained (the spin and the exact orbital contributions have been included). Third, the fitting procedure is presented and results at different levels of approximation are discussed. The main conclusions are: (1) A density built by using several molecular wave functions can give a very good agreement with the experimental data. (2) The ensemble representability constraint is necessary to retrieve physical information from the optimized parameters. (3) Taking into account the proper paramagnetic contribution to the magnetization improves significantly the agreement between theory and experiment. (4) Neglecting the diamagnetic contribution and the fact that the magnetization may be locally noncollinear to the applied external field is fully justified for the system under study. © 1996 John Wiley & Sons, Inc.     

Molecular states of atoms. II

Orbital energy parameters, previously obtained from atomic valence state energies, are used in calculating approximate wave functions for their orbitals. The radial factors of these wave functions are expressed as linear combinations of three Gaussian type orbitals with selected exponents, the coefficients being determined by normalisation and reproduction of the kinetic energy and interelectron repulsion parameters. Wave functions of universal form are obtained for the non-transition elements up to xenon. Each calculated s orbital wave function (except 1s) has a radial node, as is appropriate if there is a p orbital in the same shell with none.     

Natural orbital functional approach: Calculation of dielectric properties in molecules

Recently, we proposed a new natural orbital functional for taking into account the electronic correlation in molecular systems. Calculation of dipole moments and polarizabilities of eight selected molecules are presented. By comparison with other correlated methods, it is shown that the method has predictive capabilities for these properties. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Everyman's derivation of the theory of atoms in molecules

This paper demonstrates that it is straightforward to develop the theory of an atom in a molecule--the extension of quantum mechanics to an open system--by deriving the necessary equations of motion from Schr?dinger's equation, followed by a comparison of the predicted properties with experiment to determine the correct boundary condition. Although less fundamental than the variational derivation of the quantum theory of atoms in molecules, this heuristic approach makes the quantum mechanics of an atom in a molecule accessible to "everyman" possessing a knowledge of Schr?dinger's equation, aiding its general acceptance by experimental chemists.     

SINDO1 II. Application to ground states of molecules containing carbon,nitrogen and oxygen atoms

Molecular geometries, binding energies, ionization potentials and dipole moments are calculated by the SINDO1 method for a large number of molecules containing C, N and O atoms. Comparison is made with MINDO/3, MNDO and where possible with STO-3G results. The explicit data and an error statistics show the relative merits of SINDO1.     

Relativistic (SR‐ZORA) quantum theory of atoms in molecules properties

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density‐functional theory at both the nonrelativistic level and using the scalar relativistic zeroth‐order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc.     

On the theory of electron correlation in atoms and molecules. II. General cluster expansion theory and the general correlated wave functions method

An exact cluster expansion of many electron wave functions is derived, beginning with a finite linear combination of Slater determinants rather than the more usual single determinant. This general cluster expansion is found to apply both in the case where all possible Slater determinants from a finite set of spin orbitals are included in the linear combination, and in the case where the number of determinants is restricted. The special properties of that finite linear combination of determinants closest to the exact wave function in the least squares sense are studied. These properties lead to the derivation of a general correlated wave functions method, illustrating again the close relationship between methods of this type and cluster expansion theory. Additional approximations, necessary for practical calculations, are set out.     

Bonding and properties of superatoms. Analogs to atoms and molecules and related concepts from superatomic clusters

Expanding the versatility of well-defined clusters is a fundamental issue in the design of functional nanostructures. In this sense, the concept of super atoms allows us to gain a deeper understanding and rationalization of the different properties of metallic clusters by invoking more familiar aspects. Recently, the super atoms appear to be intimately connected to other relevant tools of great chemical significance which enhance a rational design of superatomic clusters mimicking more complex structures and networks. Here, we expect to account for the research efforts from Latin American groups in the field, highlighting their valuable contribution to superatomic and related clusters.