Approximate analytical orbital functions for second and third-row transition metals

Approximate analytical functions fors, p, d, andf orbitals of the second and third-row transition metals have been constructed from the Herman-Skillman Hartree-Fock-Slater numerical wave functions. They consist of orthonormal linear combinations of Slater-type orbital functions, and depend on a weighted least-squares criterion to judge the accuracy of the fit. The option of using a single- (one orbital function per extremum) or double- representation for the outermost maximum of a given function is included. Whereas the latter basis set is more flexible, convergence problems in the fitting method as well as an inherent arbitrariness in choosing the fitting criterion result in derived parameters which are not uniquely determined by the least-squares criterion alone.By relaxing the orthogonality requirement for orbitals of the samel and differentn it is shown that the accuracy of the fit can be significantly improved. The importance of a proper choice for the fitting criterion is discussed.

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Resume Par un critère des moindres carrés pesés, les fonctions d'onde numériques du procédé Hartree-Fock-Slater de Herman et Skillman pour les orbitaless, p, d etf des métaux de transition de la deuxième et troisième période, ont été approximées par des fonctions analytiques, soit de combinaisons linéaires orthonormées de fonctions de Slater. L'option d'employer une représentation simple- (une fonction de Slater) ou double- pour le maximum le plus éloigné d'une fonction est incluse. Quoique la seconde base soit plus flexible, des problèmes de convergence et un arbitraire inhérent de l'ajustage résultent en de paramètres non-uniques. L'ajustage s'améliore sensiblement quand l'orthogonalité des orbitales au même l est abandonnée. On discute le choix du critère d'ajustage.

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Zusammenfassung Die numerischen Hartree-Fock-Slater-Funktionen von Herman-Skillman wurden für dies-, p-, d- undf-Zustände der Übergangsmetalle der zweiten und dritten Reihe durch analytische Funktionen (Linearkombinationen von Slaterfunktionen) angendhert. Die Annäherung an die vorgegebenen Funktionen wird besser, wenn man die Orthogonalitätsbedingungen für Zustände gleicher Nebenquantenzahl fallen Iäßt.

     

Atomic natural orbital basis sets for transition metals

Summary We show that atomic natural orbitals are an excellent way to contract transition-metal basis sets, even though the different low-lying electronic states may have very different basis set requirements.     

Analysis of molecular orbital wave functions in terms of valence bond functions for molecular fragments. I. Theory

A method of expansion of molecular orbital wave functions into valence bond (VB ) functions is extended to molecular fragments. The wave function is projected onto a basis of mixed determinants, involving molecular orbitals as well as fragment atomic orbitals, and is further expressed as a linear combination of VB functions, characteristic of structural formulas of the fragment but whose remaining bonds are frozen. Structural weights for the fragment are deduced from this expression. Delocalized molecular orbitals are used as a startpoint, as they are after an ordinary SCF calculation. Wave functions of medium-sized molecules may be analyzed with reasonable storage requirements in a computer.     

The metallic orbital and the nature of metals

In 1938 it was noticed (L. Pauling, Phys. Rev.54, 899, 1938) that about 0.72 of the nine outer spd orbitals per atom of a transition metal remain unoccupied by bonding electrons, unpaired ferromagnetic electrons, or unshared electron pairs. In 1948 this 0.72 orbital per atom was identified (L. Pauling, Nature (London)161, 1019, 1948; Proc. Roy. Soc. A196, 343, 1949) as required for the unsynchronized resonance that confers metallic properties on a substance, and it was named the metallic orbital. A statistical theory of unsynchronized resonance of covalent bonds in a metal with atoms restricted by the electroneutrality principle to forming bonds only in number v ? 1, v, and v + 1, with v the metallic valence, has now been developed. This theory leads directly to the value 0.70 ± 0.02 for the number of metallic orbitals per atom, in reasonable agreement with the empirical value, and to the conclusion that M⁺, M⁰, and M^? occur in the ratios near 28:44:28. It leads also to the conclusions that stability of a metal or alloy increases with increase in the ligancy and for a given value of the ligancy is a maximum for valence equal to half the ligancy. These results with consideration of the repulsion of unshared electron pairs on adjacent atoms go far toward explaining the selection of different structures by different elemental metals and intermetallic compounds.     

Triplet correlation functions of liquid metals

An expression for the isothermal pressure derivative of the structure factor, S(q), has been obtained in the ?^?1/3 model under the mean spherical model approximation. The calculated values for liquid rubidium at 333 K and 0.43 kbar are in good agreement with the experimental observations.     

Basis sets for transition metals: Optimized outer p functions

Although the (n + 1)p orbital is unoccupied in transition-metal ground-state configurations which are all nd^x(n + 1)s^y, these (n + 1)p functions play a crucial role in the structure of transition metal complexes. As we show here, the usual solution, adding one or more diffuse functions, can be insufficient to create an orbital of the correct energy. The major problem appears to be due to the incorrect placement of the (n + 1)p orbital's node. Even splitting the most diffuse component of the np orbital and adding a second diffuse function does not completely solve this problem. Although one can usually solve this deficiency by further uncontracting of the np function, here we offer a set of properly optimized (n + 1)p functions that offer a more compact and satisfactory solution to the proper placements of the node. We show an example of the common deficiencies seen in typical basis sets, including standard basis sets in GAUSSIAN94, and show that the new optimized (n + 1)p function performs well compared to a fully uncontracted basis set. © 1996 by John Wiley & Sons, Inc.     

Simple theories for simple metals: Face-dependent surface energies and work functions

The stabilized jellium model, which preserves the simplicity of ordinary jellium while accounting for discrete-ion effects in an average way, provides an “intrinsic” surface energy and work function for each metal, determined by the mean valence electron density of the bulk. The liquid drop model asserts a dependence of the surface energy and work function on the atomic corrugation of the exposed crystal face. Together, these models are shown to make simple, quantitative predictions in good agreement with the results of all-electron calculations by Skriver and Rosengaard. Also discussed are the surface stress and the location of the image plane for stabilized jellium.     

Molecular orbital theory of the properties of inorganic and organometallic compounds. 3. STO-3G basis sets for first- and second-row transition metals

STO -3G minimal basis sets for first- and second-row transition metals have been formulated and applied to the calculation of equilibrium geometries for a variety of inorganic systems, metal carbonyls, and organometallic compounds. While the overall level of agreement with experiment is not as good as that previously noted for main-group compounds, most trends and many subtle features in geometries are reproduced.     

The influence of polarization functions on molecular orbital hydrogenation energies

Polarization functions are added in two steps to a split-valence extended gaussian basis set: d-type gaussians on the first row atoms C. N, O and F and p-type gaussians on hydrogen. The same d-exponent of 0.8 is found to be satisfactory for these four atoms and the hydrogen p-exponent of 1.1 is adequate in their hydrides. The energy lowering due to d functions is found to depend on the local symmetry around the heavy atom. For the particular basis used, the energy lowerings due to d functions for various environments around the heavy atom are tabulated. These bases are then applied to a set of molecules containing up to two heavy atoms to obtain their LCAO-MO-SCF energies. The mean absolute deviation between theory and experiment (where available) for heats of hydrogenation of closed shell species with two non-hydrogen atoms is 4 kcal/mole for the basis set with full polarization. Estimates of hydrogenation energy errors at the Hartree-Fock limit, based on available calculations, are given.

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Zusammenfassung Polarisationsfunktionen werden in zwei Schritten einer Basis von Gauß-Orbitalen hinzugefügt: d-Gauß-Funktionen für die Atome C, N, O und F und p-Gaußfunktionen für H. In allen Fällen ist ein d-Exponent von 0.8 bzw. ein p-Exponent von 1.1 bei den Hydriden befriedigend. Dabei hängt die Energieerniedrigung, die tabelliert wiedergegeben wird, von der lokalen Symmetrie am schweren Kern ab. Mit dieser Basis wird dann die LCAO-MO-SCF-Energie für Moleküle mit 2 schweren Atomen berechnet. Die mittlere absolute Abweichung zwischen Theorie und Experiment für Hydrierungswärmen von solchen Molekülen (mit abgeschlossener Schale) ist 4 kcal/Mol bei Einschluß aller Polarisationsfunktionen. Der Schätzwert für Hydrierungswärmen in der Hartree-Fock-Grenze wird ebenfalls angegeben.

     

Natural orbital analysis of nonadiabatic H2+ wave functions

Previously determined nonadiabatic wave functions for H₂⁺ (containing several hundred terms) are analyzed by using natural orbitals. This is the first time that the natural orbital concept has been applied to other than purely electronic wave functions. We find that the natural orbital expansion converges rapidly and that five or six terms are sufficient to reproduce the exact expectation values. Several plots are given of the orbitals so found and these allow a visualization of the somewhat abstract nonadiabatic wave function in a format more reminiscent of everyday quantum-mechanical pictures.     

Properties of pyridine and pyrazine from ab initio molecular orbital wave functions

Various molecular properties have been calculated for pyridine and pyrazine from Gaussian lobe ab initio SCF molecular wave functions. Values are compared with available experimental data. In general, agreement is satisfactory with the exception of the rather sensitive asymmetry parameter of the quadrupole coupling tensor. The distributions of total electronic charge, and of selected molecular orbitals have been displayed as plots of the charge density contours in two dimensions.     

Strong X-ray emission from electrified insulators.

Terasawa reported strong X-ray emission from charged-up insulators, and proposed an X-ray production device only using the electrification. We constructed a similar device and studied the conditions of X-ray emission. It was shown that X-rays could be produced without supplying electrons from a filament.     

Analytical optimization of orbital exponents in Gaussian-type functions for molecular systems based on MCSCF and MP2 levels of fully variational molecular orbital method

We have analyzed the basis function series in molecular systems by optimization of orbital exponents in Gaussian-type functions (GTFs) including the electron correlation effects with multiconfiguration self-consistent field (MCSCF) and M?ller?CPlesset second-order perturbation (MP2) methods. First, we have derived and implemented the gradient formulas of MCSCF and MP2 energies with respect to GTF exponent, as well as GTF center and nuclear geometry, based on the fully variational molecular orbital (FVMO) method. Second, we have applied these electron-correlated FVMO methods to H₂, LiH, and hydrocarbon (CH₄, C₂H₆, C₂H₄, and C₂H₂) molecules. We have clearly demonstrated that the optimized exponent values with electron-correlated methods are different from those with simple Hartree?CFock method, since adequate basis functions for adequate virtual orbitals are indispensable to describe the accurate wave function and geometry for electron-correlated calculations.     

Calixarenes functionalized with phosphine oxide and diamide functions as extractants and ionofores for rare-earth metals

Calixarene-based ligands with phosphine oxide and diamide functions at wide and narrow rims are synthesized and studied as extracting agents for liquid extraction and ionophores for polymeric electrochemical ion sensors. Calixarene ligands are compared with corresponding phosphine oxide and diamide ligands which are not attached to the calixarene platform. Extraction and sensor properties of the ligands were studied in different metal ion solution with special attention paid to rare-earth metals. Attachment of phosphine oxide groups to the calixarene platform leads to the sharp increase of both extraction and sensing ability of the corresponding systems comparing to non-bonded phosphine oxide. In case of the diamide derivatives attached to the calixarene performance of corresponding ligands was similar to those of non-bonded diamides.