Comparison of localization and delocalization indices obtained with Hartree-Fock and conventional correlated methods: effect of Coulomb correlation

Atomic populations and localization [lambda(A)] and delocalization [delta(A,B)] indices (LIs and DIs) are calculated for a large set of molecules at the Hartree-Fock (HF), MP2, MP4(SDQ), CISD, and QCISD levels with the 6-311++G(2d,2p) basis set. The HF method and the conventional correlation methods [MP2, MP4(SDQ), CISD, and QCISD] yield distinct sets of LIs and DIs. Yet, within the four conventional correlation methods the differences in atomic populations and LIs and DIs are small. Relative to HF, the conventional correlation methods [MP2, MP4(SDQ), CISD, QCISD] yield virtually the same LIs and DIs for molecules with large charge separations while LIs and DIs that differ significantly from the HF values--the LIs are increased and DIs decreased--are obtained for bonds with no or small charge separations. Such is the case in the archetypal homopolar molecules HC(triple bond)CH, H2C=CH2, CH3-CH3, and "protonated cyclopropane" C(3)H(7) (+), in which case the bonding may be atypical. Relative to HF, the typical effect of the conventional correlation methods is to decrease the DI between atoms.     

Determination of extremely localized molecular orbitals in the framework of density functional theory

Extremely localized molecular orbitals are rigorously localized on only a preselected set of atoms and do not have any tails outside the localization region. The importance of these orbitals lies in their ability to be transferred from one molecule to another one. A new algorithm to determine extremely localized molecular orbitals in the framework of the density functional theory method is presented. This could also be a valuable tool in the quantum mechanics/molecular mechanics methodology where localized molecular orbitals are used to describe covalent bonds across the frontier region. The present approach is used to build up the electron density of thymopentin, a polypeptide constituted by five residues, starting from extremely localized molecular orbitals determined on a set of model molecules. The results obtained confirm good transferability properties for these orbitals.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Moment characterization of localized orbitals

The parallel between orbital first and second electric moments and statistical first and second central moments is noted. Three measures of orbital spatial distribution in terms of their moments are proposed, and applied to the LMO's in a series of ten-electron hydrides. Consistent differences between bond and lone pair distributions are found. Using the statistical interpretation, for each LMO an effective solid angle around the central atom is postulated.     

Orbital Energy Order and the Through Bond Interaction in Homonuclear Diatomic Molecules

The homonuclear diatomic molecules are the simplest systems having both the σ framework and the lone pair orbitals n_a and _b for investigating their through space and through bond interaction. The striking orbital energy order n_g～ n_a+ n_b > n_n ～ n_a - n_b has been accounted for by the through bond interaction. However, when the p-content in the lone pair orbitals n_a and n_b decreases, one may have the reverse orbital energy order: n_g < n_g. A reverse orbital energy order has been found in F₂ and Cl₂, whose n_a and n_b are almost pure s-type atomic orbitals. The reverse order also occurs in molecule N₂ when the internuclear distance is larger man 1.5 Å. It is also found that the detail through space and through bond interaction and the eventual orbital energy order for n_g and n_u can be accounted for by the Fock operator within the localized molecular orbital space.     

An analysis of the complex molecular orbitals method

Numerical results for the ground state of the HN ₂ ⁺ and HCO⁺ molecular ions at their near equilibrium geometry, obtained by the complex molecular orbitals (CMO) method in the extended basis set, are reported. The CMO wavefunction of the HN ₂ ⁺ ion is compared with the CI wavefunction obtained in the same basis set. This reveals the nature of approximations inherent in the CMO method. A peculiar feature of the occupation numbers of the CMO natural orbitals is also explained.Alexander von Humboldt Fellow. On leave from the Institute Rudjer Bokovi, Zagreb, Croatia, Yugoslavia.     

The ab initio neglect of differential diatomic overlap method

The ab initio Neglect of Differential Diatomic Overlap (N.D.D.O.) method of Roby is tested numerically for an extensive series of molecules. Agreement with the full ab initio molecular orbital method is poor. Total energies are more negative and dipole moments are overestimated. The failings of the N.D.D.O. method are accounted for using multipole-multipole expansions.     

How Chemistry and Physics Meet in the Solid State

To make sense of the marvelous electronic properties of the solid state, chemists must learn the language of solid-state physics, of band structures. An attempt is made here to demystify that language, drawing explicit parallels to well-known concepts in theoretical chemistry To the joint search of physicists and chemists for understanding of the bonding in extended systems, the chemist brings a great deal of intuition and some simple but powerful notions. Most important among these is the idea of a bond, and the use of frontier-orbital arguments. How to find localized bonds among all those maximally delocalized bands? Interpretative constructs, such as the density of states, the decomposition of these densities, and crystal orbital overlap populations, allow a recovery of bonds, a finding of the frontier orbitals that control structure and reactivity in extended systems as well as discrete molecules.     

Oscillator Strength Calculations with the Compromised Orbitals

The oscillator strength has been calculated from a common set of compromised orbitals, instead of sets of the two separately optimized non-orthogonal orbitals for the two states involved in the transition. Inaccuracies of two types arose from the calculations were assessed by investigating simple atomic and molecular systems.     

On the role of localized molecular orbitals in the formation of bond dipoles

The hypothesis of the classical chemistry about bond dipoles resulting from shifts of separate pairs of electrons is proved using the non-canonical method of molecular orbitals (MOs). To this end, a relation is sought between the total charge distribution inside an individual chemical bond of a polyatomic molecule and the square of the respective single localized MO (LMO). General expressions for these MOs are obtained directly on the basis of the Brillouin theorem without invoking additional localization criteria. The two characteristics under comparison are presented in an explicit algebraic form in terms of meaningful components. Reshaping of square of the ‘own’ LMO of the given bond is shown to play the decisive role in the formation of secondary dipoles of initially homopolar bonds (e.g. of C–C and C–H bonds in substituted alkanes), as well as of bonds of relatively low initial polarity. Thus, representability of these dipoles by shifts of the ‘own’ pairs of electrons of respective bonds is supported. For bonds of a high initial polarity, the secondary dipoles are shown to originate mainly from contributions of LMOs of other bonds extending over the antibonding basis orbital of the given bond. Moreover, the actual secondary bond dipole takes an opposite direction vs. that predicted by the shift of the respective ‘own’ pair of electrons in this case. The latter result serves to account for the known low nucleofugality of highly electronegative heteroatoms in the S_N2 reactions.