Model potentials for molecular calculations. II. The spd-MP set for transition metal atoms Sc through Hg

Model potential parameters and valence orbitals were generated for the transition metal atoms Sc through Hg. They are named the spd-MPs and are supplementary to the sd-MPs presented in the preceding article. The outermost core np electrons were treated explicitly together with valence nd and (n + 1)s electrons, and the remaining electrons were replaced by a model potential. The model potential parameters and valence orbitals were determined in the same way as the sd-MPs. Major relativistic effects (via the mass velocity and Darwin terms) were also incorporated in the spd-MPs for the second-and third-row transition metal atoms. The results of numerical nonrelativistic Hartree-Fock (HF) calculations for the first-row transition metal atoms and of the quasirelativistic HF calculations with Cowan and Griffin's method for the second-row and third-row transition metal atoms were used as reference data in determination of the spd-MPs.     

Why do the second row transition metal atoms prefer 5s14dm+1 to 5s24dm?

Numerical Hartree-Fock (NHF) calculations have been performed for 332 ground and low-lying excited states of the fifth period atoms Rb through Xe, with our special interest in the states arising from the 5s ²4d ^m , 5s ¹4d ^m +1, and 5s ⁰ 4d ^m +2 configurations of the second row transition metal atoms. Among various properties, orbital energies and mean values ofr of the outermost orbitals of each symmetry are presented as well as total energies. It is discussed in some detail why the second row transition metal atoms have a tendency to prefers ¹ d ^m +1 as the ground configuration in contrast to the preferreds ² d ^m configuration in the first row transition metal atoms. Our systematic NHF computations reported in this and the previous papers conclude that the Hartree-Fock method correctly predicts the experimental ground state of the atoms He through Xe with the sole exception for Zr.     

An Anomalous Electron Configuration Among 3d Transition Metal Atoms

Physical properties of materials are mainly determined by valence electron configurations, where different valence shells would induce divergent phenomena. In compounds containing Sc²⁺, 3d electron occupancy is expected, the same as other transition metal atoms like Ti³⁺. But this situation still awaits experimental verification in inorganic materials. Here, we selected ScS to measure the valence electron density and orbital population of Sc²⁺ through delicate quantitative convergent-beam electron diffraction. With the absence of 3d orbital features around Sc-atom sites and the nearly bare population of t_2g orbital, the unintuitive occupation of 4s orbital in Sc²⁺ is concluded. It should be the first time to report such a special electron configuration in a transition metal compound, in which 4s rather than 3d orbital is preferred. Our findings reveal the distinct behavior of Sc and probable ways to modulate material properties by controlling electron orbitals.     

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.     

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.     

Electric-field gradient calculations for atoms with axial symmetry

Restricted open-shell Hartree-Fock and unrestricted Hartree-Fock calculations of the electric-field gradient in atoms B, N, O, Al, S, and Cl were performed by relieving the spherical symmetric constraint. The Sternheimer's core polarization effect is then automatically taken into account. The orbitals produced by the axial symmetric self-consistent field are found to have axial symmetry of s-d and p-f mixing types. However, the nonequivalence of the three p orbitals also gives rise to ambiguity. © 1996 John Wiley & Sons, Inc.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsd ⁿ ,d ^n–1 s, andd ^n–2 s ² for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.     

Compact basis sets for LCAO-LSD calculations. Part I: Method and bases for Sc to Zn

A method for preparing compact orbital and auxiliary basis sets for LCAO-LSD calculations has been developed. The method has been applied to construct basis sets for first row transition metal atoms from Sc to Zn for the 3d^n?14s¹ and 3d^n?24s² configurations. The properties of different expansion patterns have been tested in atomic calculations for the chromium atom.     

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.     

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.     

Basis set quality versus size II. Approximate GTO wave functions for second row transition metal atoms

Basis sets ranging in size from (16, 10, 7) to (20, 14, 11) have been derived for the atoms Y–Cd. Separate sets represent the energy optimized wave functions for each of the s²dⁿ, s¹dⁿ⁺¹, and s⁰dⁿ⁺² configurations. The energies from the largest sets are within 3 mhartrees of the values obtained in numerical Hartree–Fock calculations. Reasonable Hartree–Fock s²dⁿ– s¹dⁿ⁺¹ and s²dⁿ– s⁰dⁿ⁺² excitation energies may be obtained either using the largest basis sets, or using d-orbitals optimized for the s⁰dⁿ⁺² configurations. The basis sets are slightly unbalanced in favor of the s-functions and in disfavor of the d-functions, but various alternative basis sets may be derived by combining parts of the five parent sets. The convergence of radial expectation values is discussed.     

Manganese hydride potential energy curves

The potential energy curves of the ⁷Σ⁺ and the ⁵Σ⁺ states of MnH are calculated using restricted Hartree-Fock, unrestricted Hartree-Fock and the perfect pairing generalized valence bond methods. Both of these states are bound, with the ⁷Σ⁺ lowest in energy. The bonding for both states is to the 4s² shell rather than to any of the five singly occupied d orbitals. The MnH bonding orbitals are sp hydribs. These results are compared to similar studies of H on Sc, Fe, Ni and Cu. The implications of these results to hydrocarbon catalysis by first row transition metal catalysis are considered.     

Valence 4p functions for the first-row transition metal atoms

For the valence 4p orbitals of the first-row transition metal atoms Sc through Zn, Gaussian-type basis functions are developed referring to excited 3d ^m 4s ¹4p ¹ electronic configurations. Molecular tests of the present work 4p sets are performed for the Cu atom, the diatomic Cu₂ molecule, and Cu₉ and Cu₁₃ clusters, and the results are compared with those from two literature sets. Received: 17 January 2000 / Accepted: 30 May 2000 / Published Online: 11 September 2000     

Applications of spectral-Representation model as a potential method for Cu clusters

We applied the spectral-representation technique developed by Katsuki and Huzinaga as a model potential in calculating the electronic structure of Cu clusters. The characteristics of this potential were closely investigated in Cu and Cu₂. For Cu, Cu₂, Cu₅, Cu₉, and Cu₁₃, we performed all-electron ab initio self-consistent field calculations and model-potential calculations where 3p, 3d, and 4s electrons, and 3d and 4s electrons are treated as valence electrons. The ionization potentials (IPs) given by the all-electron calculations were 6.26, 5.55, 4.52, 4.02, and 4.08 eV for Cu, Cu₂, Cu₅, Cu₉, and Cu₁₃, respectively. The IPs given by the model-potential calculations were 6.25, 5.56, 4.62, 4.09, and 4.23 eV for the 3p-, 3d-, and 4s-valence electrons, and 6.26, 5.68, 4.71, 4.07, and 4.19 eV for the 3d- and 4s-valence electrons. The IPs given by the model-potential calculations agree well with those of the all-electron calculations. We also performed model-potential calculations where only the 4s electrons were treated as valence electrons. The calculated IPs were 6.47, 5.98, 5.38, 4.63, and 4.88 eV for Cu, Cu₂, Cu₅, Cu₉, and Cu₁₃, respectively. These are ca. 0.8 eV higher than the IPs by the all-electron calculation for the larger clusters of Cu₅, Cu₉, and Cu₁₃. The higher IPs originate from the expulsion of the 3d electrons from the valence electrons. We also performed model-potential calculations with 4s electrons for Cu₇₄. The calculated IP is 4.61 eV, which is estimated to be 0.8 eV larger than that obtained by the all-electron calculation. The IPs with correlation corrections are 7.7, 7.4, 6.3, 5.8, 5.9, and 5.6 eV for Cu, Cu₂, Cu₅, Cu₉, Cu₁₃, and Cu₇₄, respectively. Experimental values are 7.73, 7.37, 6.30, 5.37, 5.67, and 5.26 eV. The agreement between the two is fairly good. The electron affinities are also discussed. © 1996 by John Wiley & Sons, Inc.     

Electronic states of NiFe. Anab initio HF-CI study

Ab initio Hartree-Fock and configuration interaction methods have been employed in describing the interaction between a Ni and an Fe atom. The chemical bond between the atoms is due to a 4sσ molecular orbital. The 3d orbitals merely cause small splittings between the potential energy curves. Equilibrium distance, dissociation energy and vibrational frequency are predicted for the ground state of the molecule.     

On incorporation of atomic correlation in transition-metal molecular calculations: NiH

The atomic correlation terms necessary to lead to anaccurate 4s²3d⁸-4s^t 3d⁹ separation for the Ni atom have been incorporated into all-electron MC SCF/Cl calculations for the X² Δ state of NiH. The calculated potential curve properties are significantly improved compared to calculations which dissociate to Hartree-Fock atoms.     

Investigation of the use of density functionals in second‐ and third‐row transition metal dimer calculations

We explore the use of density functionals in calculating the equilibrium distances, dissociation energies, and harmonic vibrational frequencies of the homonuclear diatomics of the second‐row transition metals, platinum, and gold. The outermost s–d interconfigurational energies (ICEs) and the outermost s and d ionization potentials (IPs) were also calculated for the second‐ and third‐row transition metal atoms. Compared with the first‐row transition metal dimer calculations (J Chem Phys 2000, 112, 545–553), the binding energies calculated using the combination of the Becke 1988 exchange and the one‐parameter progressive correlation (BOP) functional and Becke's three‐parameter hybrid (B3LYP) functional are in better agreement with the experiment. However, the pure BOP functional still gives the deep and narrow dissociation potential wells for the electron configurations containing high‐angular‐momentum open‐shell orbitals. Analysis of the s–d ICEs and the s and d IPs suggests that the overestimation may be due to the insufficient long‐range interaction between the outermost s and d orbitals in the exchange functional. The hybrid B3LYP functional seems to partly solve this problem for many systems by the incorporation of the Hartree–Fock exchange integral. However, this still leads to an erroneous energy gap between the configurations of fairly different spin multiplicity, probably because of the unbalance of exchange and correlation contributions. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1995–2009, 2001