A systematic preparation of new contracted Gaussian-type orbital sets. VI. Ab initio calculation on molecules containing Na through Cl

Compact contracted Gaussian basis sets introduced in the preceding article are tested for ab initio molecular calculations on molecules containing third-row atoms (Na through Cl). It is found that the effect of splitting valence orbitals is essential for these molecules and addition of polarization functions to split basis sets can yield computed geometries, spectroscopic constants, and atomization energies in close agreement with the result of near Hartree–Fock calculations.     

过渡金属体系非线性光学性质计算的ECP基组研究

有效核势(ECP)方法是计算含有过渡金属体系的电子结构及物理性质的有效方法. 本文比较了一系列典型的ECP基组对计算含过渡金属体系非线性光学性质精度的影响. 分别在HF, MP2和DFT理论水平上对过渡金属元素使用不同的ECP基组, 计算了几个过渡金属有机化合物的静态一阶超极化率β₀. 研究结果表明: 使用有效核势计算含过渡金属体系时, 核电子的选取是提高计算精度的前提, ns和np电子应该和nd电子一同作为价电子处理; 对于重原子, 必须考虑自旋-轨道耦合相对论效应. 经过综合评估, 认为使用Stuttgart/Dresden赝势的ECP基组, MHF, 在计算含有过渡金属体系非线性光学性质方面是比较好的基组; Stuttgart RSC 1997和SBKJC VDZ相对而言是较好的基组; 基组Lanl2dz, Hay-Wadt MB (n＋1)和Hay-Wadt VDZ (n＋1)由于没有考虑自旋-轨道耦合, 计算精确度次之; 而基组CRENBL和CRENBS计算的偏差要大一些, 尤其是CRENBS基组由于价电子选择得太少而导致与实验值的偏差最大.     

Nonempirical parameters of the nonlocal core pseudopotential for the second and third row elements

For the core pseudopotential (CP) model constructed in terms of Bonifacic-Huzinaga nonlocal CP theory, parameters of the local component of CP are calculated for the second-and third-row elements. The resulting CP are associated with the Coulomb, exchange, and correlation potentials created by the nuclear charge and electron density of the core electrons. The electronic structure and potential energy surface are calculated for the hydrides of the second-row elements (LiH, CH₄, NH₃, H₂O, HF); the calculations are performed by the nonempirical nonlocal CP method. The results of these calculations agree well with those of SCF MO LCAO ab initio calculations and with experimental data.     

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.     

Electronic structures of multi-decker transition metal sandwich complexes

The electronic structures of multi-decker transition metal sandwich complexes are discussed according to the structure rules for transition metal heterocarboranes. A series of skeletons of the structures Fe₂C₅(D_5h), Ni₂C₅(D_5h), V₂C₆(D_6h), Co₂C₆(D_6h), and Fe₂C₄(D_4h) are calculated using the EHMO method. The calculated results show that the number of valence bonding orbitals (VBO) can vary as the distance between the metal atoms in the metalocenes is increased. This fact can be used to explain the number of valence electrons (VE) in triple-decker sandwich complexes. The conclusions are proved and discussed through a theoretical analysis of the electronic structures of such complexes and through EHMO calculations for actual compounds containing 29–34 valence electrons.     

The structures of transition metal-transition metal alloys

A structure map using the average electron count and d orbital energy difference as indices is used to sort transition metal alloys of stoichiometry AB. The gross features of the map are mimicked by tight-binding calculations. The inclusion of s orbitals on the metal atoms appear to be important in the determination of alloy structure in some parts of the calculated map. The correct coloring of the elemental lattice as a function of electron count is reproduced by calculation (i.e., AuCd vs WC and CsCl vs CuTi). Two new stability fields for the WC and CuTi structures are predicted. The calculations fail to really distinguish bcc, fcc, and hcp derivative structures in the region of 6–8 d + s valence electrons per atom. In this part of the structure map the calculations appear to be sensitive to small geometrical changes.     

On the role of d electrons in chemisorption and catalysis on transition metal surfaces

A new model is proposed for the role of the d electrons in chemisorption and catalysis on transition metal surfaces. In this model, the d electrons remain localized on the atoms and do not participate in forming dsp hybrid bonds with the adsorbate. However, electrons in doubly-occupied d orbitals can be promoted to anti-bonding or non-bonding valence orbitals. These additional electronic configurations help increase the binding energy of the adsorbate and help stabilize reaction intermediates. This effect is enhanced by spatial rotation of the singly-occupied d orbitals which become perpendicular to the adsorbate. The singly-occupied d orbitals are also able to recouple their spins during the reaction, allowing the reaction to proceed on otherwise forbidden reaction paths.     

Energy-adjustedab initio pseudopotentials for the second and third row transition elements

Summary Nonrelativistic and quasirelativisticab initio pseudopotentials substituting the M^(Z–28)+-core orbitals of the second row transition elements and the M^(Z–60)+-core orbitals of the third row transition elements, respectively, and optimized (8s7p6d)/[6s5p3d]-GTO valence basis sets for use in molecular calculations have been generated. Additionally, corresponding spin-orbit operators have also been derived. Atomic excitation and ionization energies from numerical HF as well as from SCF pseudopotential calculations using the derived basis sets differ in most cases by less than 0.1 eV from corresponding numerical all-electron results. Spin-orbit splittings for lowlying states are in reasonable agreement with corresponding all-electron Dirac-Fock (DF) results.     

Compact contracted Gaussian-type basis sets for halogen atoms. Basis-set superposition effects on molecular properties

Compact, contracted Gaussian basis sets for halogen atoms are generated and tested in ab initio molecular calculations. These basis sets have similar structure to that of Huzinaga and co-workers' (HTS ) sets; however, they give both better atomic total energies and better properties of atomic valence orbitals. These sets, after splitting of valence orbitals and augmenting with polarization functions, provide molecular results that agree well with those given by extended calculations. Basis set superposition error (BSSE ) is calculated using the counterpoise method. BSSE has only slight influence on calculated equilibrium geometry, shape of potential curve, and electric properties (dipole and quadrupole moments) of molecules. However, atomization energies may be significantly changed by the BSSE .     

Ab initio Hartree-Fock calculations of molecular X-ray intensities. Validity of one-center approximations

Ab initio Hartree-Fock calculations of relative X-ray transition probabilities for core hole states of N₂, CO, H₂O and NH₃ have been carried out and compared with the respective high-resolution soft X-ray spectra. The same one-determinental wavefunctions were employed for both initial and final states and the dependence of the X-ray transition moments on the choice of orbitals and of basis set parameters was investigated. In particular, orbitals optimized for a transition state were tested. The use of the one-center intensity model as a guide for the assignment of second row X-ray spectra was justified at bothab initio and semiempirical (CNDO) levels of approximation. The breakdown of the MO-picture for inner-valence electrons is demonstrated in the X-ray spectrum of N₂ and the analogy with the corresponding photoelectron bands is pointed out.     

A note on the importance of d orbitals in the calculation of effective interactions and the excitation spectra of atoms and molecules

The focal point of our discussion is the examination of truncated basis sets used in obtaining an accurate first principles clculation of the effective valence shell Hamiltonian by the canonical transformation-cluster expansion approasch. Subsequent diagonalization of this effecitve valence shell hamiltonian yields the valence shell transition energies. A detailed analysis of numerical results obtained using a number of different basis sets of hydrogen-like orbitals together with rigorous symmetry arguments celarly demonstrates the special role played by d orbitals in computing the ³P → ¹D transition energy in carbon. The failure of early attempts to calculate the effective Hamiltonian for ethylene from first principles is examined in the light of recent ab initio calculations on ethylene involving d orbitals and the computations reported in this paper. We conclude that accurate calculations of the effective valence shell Hamiltonian for molecules must consider d orbitals in the excited orbital basis set.     

Electronic structure,chemical bonding,and oxidation numbers of first‐row transition metals in [MePIm2] complexes and their cations

The qualitative structures of the upper one‐electron energy levels of imidazole‐coordinated first‐row transition metal porphyrin [MePIm₂] complexes established in the present study have shown that the second oxidation number of the first‐row transition metals in the neutral complexes do not change in their cations and double cations. It was found that occupied orbitals of the density functional theory method obtained with B3LYP functional are not correctly ordered. Therefore, they cannot be used in investigations of the orbital structure of the upper molecular orbitals. A qualitative analysis of density functional theory method wave functions in terms of Mulliken and natural charges of atoms, together with an analysis of electrostatic potentials of the neutral [MePIm₂] complex, its single and double cations, demonstrates that the highest occupied orbitals of these complexes are mainly formed by atomic orbitals of the porphyrin ring atoms. Therefore, transition metal atoms are not active in chemical reactions with these complexes unless the 3d electrons of transition metal atoms are excited, for example by light. A mechanism of an electron transfer reaction that occurs between a heme cytochrome and Fe‐oxide mineral surface is discussed in the light of the obtained results. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Unified interpretation of Hund's first and second rules for 2p and 3p atoms

A unified interpretation of Hund's first and second rules for 2p (C, N, O) and 3p (Si, P, S) atoms is given by Hartree-Fock (HF) and multiconfiguration Hartree-Fock (MCHF) methods. Both methods exactly satisfy the virial theorem, in principle, which enables one to analyze individual components of the total energy E(=T+V(en)+V(ee)), where T, V(en), and V(ee) are the kinetic, the electron-nucleus attraction, and the electron-electron repulsion energies, respectively. The correct interpretation for each of the two rules can only be achieved under the condition of the virial theorem 2T+V=0 by investigating how V(en) and V(ee) interplay to attain the lower total potential energy V(=V(en)+V(ee)). The stabilization of the more stable states for all the 2p and 3p atoms is ascribed to a greater V(en) that is caused by contraction of the valence orbitals accompanied with slight expansion of the core orbitals. The contraction of the valence orbitals for the two rules is a consequence of reducing the Hartree screening of the nucleus at short interelectronic distances. The reduced screening in the first rule is due to a greater amount of Fermi hole contributions in the state with the highest total spin-angular momentum S. The reduced screening in the second rule is due to the fact that two valence electrons are more likely to be on opposite sides of the nucleus in the state with the highest total orbital-angular momentum L. For each of the two rules, the inclusion of correlation does not qualitatively change the HF interpretation, but HF overestimates the energy difference ∣ΔE∣ between two levels being compared. The magnitude of the correlation energy is significantly larger for the lower L states than for the higher L states since two valence electrons in the lower L states are less likely to be on opposite sides of the nucleus. The MCHF evaluation of ∣ΔE∣ is in excellent agreement with experiment. The present HF and MCHF calculations demonstrate the above statements that were originally given by Katriel [Theor. Chem. Acta 23, 309 (1972); 26, 163 (1972)]. We have, for the first time, analyzed the correlation-induced changes in the radial density distribution for the excited LS terms of the 2p and 3p atoms as well as for the ground LS term.     

The Valence Orbitals of the Alkaline-Earth Atoms

Quantum chemical calculations of the alkaline-earth oxides, imides and dihydrides of the alkaline-earth atoms (Ae=Be, Mg, Ca, Sr, Ba) and the calcium cluster Ca₆H₉[N(SiMe₃)₂]₃(pmdta)₃ (pmdta=N,N,N′,N′′,N′′-pentamethyldiethylenetriamine) have been carried out by using density functional theory. Analysis of the electronic structures by charge and energy partitioning methods suggests that the valence orbitals of the lighter atoms Be and Mg are the (n)s and (n)p orbitals. In contrast, the valence orbitals of the heavier atoms Ca, Sr and Ba comprise the (n)s and (n−1)d orbitals. The alkaline-earth metals Be and Mg build covalent bonds like typical main-group elements, whereas Ca, Sr and Ba covalently bind like transition metals. The results not only shed new light on the covalent bonds of the heavier alkaline-earth metals, but are also very important for understanding and designing experimental studies.     

Enhanced Zintl anions by carbon doping in Al-Na clusters and new magic structure Al6Na4C

This article investigated the low-energy structures of Al₆Na _mC (m = 2, 4, 6, 8) clusters and their electronic structures by using genetic algorithm combined with density functional theory and configuration interaction methods. The computations show that the C atoms prefer sitting at the center, whereas the Na atoms tend to locate at the outside of the clusters. The valence molecular orbitals (MOs) agree well with the prediction of the jellium model. The stronger attraction of the central carbon to the valence electrons will depress the potential energies locally, which makes the 2S level go obviously lower and the 2P and 1D orbitals form a sub-band. The 26 valence electrons in Al₆Na₄C form closed 1S²1P⁶2S²1D¹⁰2P⁶ shells and correspond to a new magic structure. The MOs and electron localization function show that the sodium cores are exposed at the outside of the valence electrons and form naked cations. The contraction of the valence electrons because of the carbon doping enhances the charges on the Al₆C moieties, and the Na⁺ cores on the peripheries are ionically bonded to the Zintl anions (Al₆C)^q−. The Al₆Na₄C has a tetrahedral structure with symmetry T_d, and it may be used as building blocks to synthesize Zintl solid.     

Halogénures Alcalins: Un Modèle Incluant une Délocalisation à Courte Distance Application à la Stabilité Relative des Divers Arrangements Cristallins

The introduction of symmetry-adapted hybrid atomic orbitals on the metallic atoms allows us to divide the crystal into elementary cells which contain 8 valence electrons each. These cells are described by linear combinations of the halogen valence shell s and p orbitals and the hybrid orbitals of the nearest metallic atoms which point to the halogen. The electronic delocalization of the halogen ions is very weak (?0.02) for: LiF, NaF, KF, LiCl, NaCI, and KCI. The cell energy in the crystal is obtained by using a first-order perturbative treatment. In agreement with experiment, the f.c.c. type is found more stable than the b.c.c. or the blende type.     

Valence p functions for alkali and alkaline-earth atoms

Contracted Gaussian-type function (CGTF) basis sets are reported for valence p orbitals of the six alkali and alkaline-earth atoms Li, Be, Na, Mg, K, and Ca for molecular applications. These sets are constructed by Roothaan–Hartree–Fock calculations for the ns → np excited states of atoms, in which both linear and nonlinear parameters of CGTFs are variationally optimized. The present CGTF sets reproduce well the numerical Hartree–Fock ns → np excitation energies: the largest error is 0.0009 hartrees for Li. New CGTFs are tested with diatomic Li₂, Na₂, K₂, and MH molecules, where M = Li, Be, Na, Mg, K, and Ca, by self-consistent-field (SCF) and multiconfiguration SCF calculations. The resultant spectroscopic constants compare well with those of more elaborate calculations and are sufficiently close to experimental values, supporting the efficiency of the present set for the valence p orbitals. Received: 9 July 1998 / Accepted: 17 September 1998 / Published online: 1 February 1999