The floating spherical gaussian orbital model and shape of B2H5 ion

The FSGO model has been used to make ab initio calculations of the geometry of B₂H ion. The results indicate that the acetylenic structure has the lowest energy (?43.881 a.u.) and the planar structure has the highest energy (?43.838 a.u.). The energy of the non-symmetric structure is only slightly higher (?43.879 a.u.) than that of the acetylenic one. Results of CNDO /2 calculations reported here also predict the acetylenic structure to be the most stable one.     

A molecular orbital approach to electronegativity equalization

From the basic premises of Molecular orbital theory it is shown that the various electronegativity equalization theories, at present in the literature, are fundamentally the same, and are expressable in a unified theory, developed herein. General relationships are established for calculating equilibrated electronegativities, electron densities and extra ionic resonance energies. The Equalization method is related to other methods for calculating the properties of localized bonds in molecules.

---

Zusammenfassung Auf der Grundlage der MO-Theorie werden die verschiedenen bekannten Theorien des ElektronegativitÄtsausgleichs im Rahmen einer Theorie dargestellt. Allgemeine Regeln zur Berechnung ausgeglichener ElektronegativitÄten, Elektronendichten und der zusÄtzlichen ionischen Resonanzenergien werden angegeben. Die Methode des ElektronegativitÄtsausgleichs wird mit anderen Methoden zur Berechnung der Eigenschaften lokalisierter Bindungen in Molekülen verknüpft.

---

Résumé On montre, à partir des fondements de la théorie des orbitales moléculaires, que les diverses théories d'égalisation de l'électronégativité, qui ont actuellement cours, sont essentiellement les mÊmes et peuvent Être exprimées dans une théorie unifiée développée ci-après. Des relations générales sont établies pour calculer les électronégativités égalisées, les densités électroniques et oes énergies de résonance ionique supplémentaires. La méthode d'égalisation est reliée aux autres méthodes de calcul des propriétés des liaisons localisées dans les molécules.

     

Floating spherical gaussian orbital open-shell calculations on the four-electron H4 system

Floating spherical Gaussian orbital (FSGO ) open-shell calculations have been made to determine the potential energy surface of planar square and rectangular arrangements of the four-electron system H₄. This surface is discussed in relation to the bimolecular isotope exchange reaction H2+D2-→ 2HD. The changes in energy and geometry accompanying the coplanar approach of two hydrogen molecules interacting chemically have also been investigated. Calculations on the electronic energies of planar T-shaped and kite arrangements of H4 of various sizes show that it is unlikely that these configurations can serve as transition states for the exchange reaction. However, the energy curve for linear configurations of H4 (H? H? H … H), calculated as a function of the H₃ … H distance with the symmetric linear H₃ (H-H-H) unit fixed at the internuclear distance of 1.9080 a.u., is found to have a deep minimum (?1.9176 a.u.) at an r(H₃ … H) distance of 1.5846 a.u. The overall results suggest that the following mechanism for the exchange reaction, H₂+H₂→H₂+H+H→H₃+H→H+H₂+ H→H₂+H₂ could be advantageous as it requires a barrier height of 0.1604 a.u. which is significantly lower than that calculated from the saddle point energy (0.1950 a.u.). However, the problem of reconciling this with the experimental activation energy of 0.0685 a.u. still remains.     

A floating spherical Gaussian orbital model of molecular structure

The FSGO model has been used to make ab initio calculations of the geometrical structures of borazane and diborane. Where experimental data are available there is good agreement between calculated and observed values.

---

Zusammenfassung Für ab initio-Rechnungen zur geometrischen Struktur des Borazans und Diborans wurde das FSGO-Modell benutzt. Soweit experimentelle Werte vorhanden sind, stimmen die berechneten und beobachteten Werte gut überein.

---

Résumé La méthode FSGO a été utilisée pour effectuer des calculs ab-initio sur les structures géométriques du borazane et du diborane. Un bon accord est obtenu entre les valeurs calculées et les valeurs expérimentales existantes.

     

Capability of pseudopotential methods to simulate all-electron calculations with floating spherical gaussian orbitals

A pseudopotential method has been applied to the calculation of local molecular orbitals for the water molecule in its ground state. Calculated values of the bond length and of the bond angle are in good agreement with those obtained from analogous calculations involving all the electrons. Comparison with experimental data is of the same quality in the two types of calculations.     

Analytical second derivatives of molecular electronic energy integrals obtained by spherical gaussian orbital

In this research, the complete general formulas for the analytical second derivative of the molecular integrals for spherical gaussian orbitals of electronic energy are presented. Formulas were given for the second derivative for orbital exponent, orbital and nuclear cartesian coordinates and coefficients of contracted gaussians. In order to save computational time, the formulas for the second derivative are written in terms of the original integrals. Although the formulas were presented in general for any type of application, the Floating Spherical Gaussian Orbital (FSGO) method is applied to some molecules such as LiH, H₂O and CH₂ (singlet) to check the formulas. The results were compared with the results of the finite difference method. Besides the accuracy of the analytical derivative, the saving in computational time is significant.     

A floating spherical gaussian orbital model of molecular structure. XII. Analysis of energy terms affecting the geometry of the water molecule

The energy terms arising in the water calculation by the FSGO method are analyzed as a function of the bond angle in order to gain insight into the reasons for the particular equilibrium configuration. The analysis is made in terms of symmetrically orthogonalized orbitals so as to exclude three- and four-orbital electron repulsion terms.     

Extended floating spherical gaussian basis sets for molecules. Generation procedure and result for H2O

A procedure is proposed to generate extended floating spherical gaussian orbital (FSGO) basis sets for molecular SCF calculations by projecting large basis set SCF results onto FSGOs. This replaces the need for repeated evaluation of energy integrals and SCF iterations for extensive non-linear optimizations of FSGOs.     

Floating spherical gaussian orbital (FSGO) studies with a model potential: some open-shell systems

A gaussian based model potential is used within the FSGO formalism to study a series of open-shell systems (e.g. LiH⁺, NaH⁺, Li⁺₂ and LiNa⁺). Results for calculated equilibrium geometries and dissociation energies are compared to the corresponding quantities from available all-electron ab initio studies and other more elaborate theoretical estimates. The overall agreement is quite satisfactory.     

Fluctuations in electronegativity and global hardness induced by molecular vibrations

A pair of novel molecular indices has been proved to contain important information on the coupling between atomic displacement and electronic properties based on the electron density function within the Density Functional Theory: the nuclear reactivity (Φ) and nuclear stiffness (G). Appropriate calculation procedure has been developed and their role in describing anharmonicity of diatomic molecules has been demonstrated. This present work provides analysis of this effect for small molecules, unveiling the role of symmetry of molecular vibrational modes in modifying the affinity of a molecule to intermolecular electron transfer. The indices have been found to be a crucial factor determining thermal fluctuations in the molecular energy derivatives: electronegativity (χ) and hardness (η). The fluctuations of hardness play a specific role, as they bring a molecule uniquely to a critical region (η0), when molecule becomes unstable to an electron exchange process, due to its excitation in a selected destructive vibrational mode.     

Floaing spherical gaussian orbital (FSGO) studies with a model potential: Some alkali halides

A gaussian based model potential is used in the framework of the FSGO approach to study the equilibrium geometries, force constants and charge distributions of some alkali halides (LiF, LiCl, NaF, NaCl, KF and KCl). The predicted results are in good agreement with the available experimental data and the results of other ab-initio studies.     

Atomic charges based on spherical harmonics expansion at the atomic centers

Molecular orbitals are expanded in spherical harmonics functions around atomic centers. The expansion coefficient is a function of the distance from the nucleus and the quotient between this function and a corresponding atomic orbital is almost constant in the core region. The square of the quotient is used as a definition of an atomic charge component. The erratic dependence on the type of basis functions in the Mulliken method is thereby avoided. The relationship between the new charge and the Mulliken population is investigated and a new invariant Mulliken population is suggested.     

Modeling continuous changes in substituent electronegativity and chemical hardness using fictitious nuclear potentials

The performances of a family of recently developed generalized gradient approximation (GGA) functionals based on the Tognetti–Cortona–Adamo (TCA) family and making use of the gradient-regulated connection (GRAC) approach are here tested on an uncommon benchmark set for the prediction of transition state (TS) structures and energies of a series of four reactions involving an early transition metal (Zr, d ⁰). This benchmark test thus represents the first step in the organometallic world in which d ⁿ ions allowing complex phenomena such as spin crossover represent the higher level of complexity. The results obtained show that the performances of the GRAC-xxx functionals are comparable to those of global hybrid functionals both in the prediction of reaction barriers and of structural features of TSs. More complex functional forms (such as range-separated hybrids) in average enhance the energetic features, but not necessarily the overall accuracy on calculated structures. On the other hand, and as expected, purposely developed functionals for the prediction of chemical reactivity provide both structural and energetic features in good agreement with post-HF results. The present study, besides proving the good performances of GGA functionals of the GRAC-TCA family for the prediction of TS structural parameters and energetics of metal containing systems, also underlines the importance of the use of diversified benchmark sets to allow a fair evaluation of functionals performances.     

Systematic formulations for electronegativity and hardness and their atomic scales within density functional softness theory

A unified Mulliken valence with Parr ground‐state electronegativity picture is presented. It provides a useful analytical tool on which the absolute hardness as well ionization potential and electron affinity functionals are based. For all these chemical reactivity indices, systematic approximate density functionals are formulated within density functional softness theory and are applied to atomic systems. For the absolute hardness, a special relationship with the new electronegativity ansatz and a particular atomic trend paralleling the absolute electron affinity are established that should complement and augment the earlier finite‐difference energetic approach. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Floating spherical gaussian orbital model study of some organometallic systems. I. LiCH3, HBeCH3, and CH3BeCH3

The floating spherical Gaussian orbital method has been used to study the equilibrium geometries and electronic structures of some organometallic systems like LiCH₃, HBeCH₃, and CH₃BeCH₃. The predicted geometries are in good agreement with other theoretical estimates and available experimental results. Electron transfer values from carbon to metal atom and bond energies of Li? C and Be? C bonds are estimated and discussed. The wave functions obtained here have also been used to predict the electron momentum distributions and Compton profiles for LiCH₃, HBeCH₃, and CH₃BeCH₃.     

Atomic orbitals in molecules: general electronegativity and improvement of Mulliken population analysis

An approach of atomic orbitals in molecules (AOIM) has been developed to study the atomic properties in molecules, in which the molecular orbitals are expressed in terms of the optimized minimal atomic orbitals. The atomic electronegativities are calculated using Pauling's electronegativity of free atom and are employed to find the electronegativity equilibrium in molecules and to describe the amphoteric properties of the transition metals from the groups 4 to 10. AOIM can also improve the numerical stability and accuracy of the original Mulliken population analysis.     

A quick solvation energy estimator based on electronegativity equalization

ESE-EE (Easy Solvation Estimation with Electronegativity equalization) is a quick method for estimation of solvation-free energies ΔGº_solv, which uses a thoroughly fitted electronegativity equalization (EE) scheme to obtain atomic charges, which are further employed in a scaled noniterative COSMO-like calculation to evaluate the electrostatic component of ΔGº_solv. Nonelectrostatic corrections including adjustable parameters are also added. For neutral solutes, ESE-EE yields a mean absolute error (MAE) in ΔG_solv° of 1.5 kcal/mol for aqueous solutions; 1.0 kcal/mol for nonaqueous polar protic solvents; 0.9 kcal/mol for polar aprotic solvents; and about 0.6 kcal/mol for nonpolar solvents. Since ESE-EE only requires a molecular geometry as input for a ΔGº_solv prediction, it can be utilized for a rapid screening of ΔGº_solvfor large neutral molecules. However, for ionic solutes, ESE-EE yields larger errors (typically several kcal/mol) and is recommendable for preliminary estimations only. Upon a special refitting, ESE-EE is able to yield partition coefficients with a good accuracy.