Structure and properties of transition-metal compounds. A systematic study of basis set effects in ab initioSCF calculations

The recently developed Gaussian basis functions [2] were used in calculations on the ground electronic states of molecules containing transition-metal atoms: ScF₃, TiCl₄, ZrCl₄, Cr(CO)₆, Ni(CO)₄, CuF, CuCl, Zn(CH₃)₂, and Cd(CH₃)₂. The usefulness of minimal basis sets, the importance of splitting of the valence part of the minimal basis sets, the role of the triple splitting of the d-block functions, and the need for p-, d-, and f-type polarization functions were discussed in the context of the geometrical structure and the firstorder electronic properties of the transition-metal atom compounds.     

Medium-size Gaussian basis sets for hydrogen through argon

Summary Medium-sized Gaussian basis sets are reoptimized for the ground states of the atoms from hydrogen through argon. The composition of these basis sets is (4s), (5s), and (6s) for H and He, (9s5p) and (12s7p) for the atoms Li to Ne, and (12s8p) and (12s9p) for the atoms Na to Ar. Basis sets for the² P states of Li and Na, and the³ P states of Be and Mg are also constructed since they are useful in molecular calculations. In all cases, our energies are lower than those obtained previously with Gaussian basis sets of the same size.     

Optimization of Gaussian basis sets for Dirac-Hartree-Fock calculations

We investigate the optimization of Gaussian basis sets for relativistic calculations within the framework of the restricted Dirac-Hartree-Fock (DHF) method for atoms. We compare results for Rn of nonrelativistic and relativistic basis set optimizations with a finite nuclear-size. Optimization of separate sets for each spin-orbit component shows that the basis set demands for the lower j component are greater than for the higher j component. In particular, the p _1/2 set requires almost as many functions as the s _1/2 set. This implies that for the development of basis sets for heavy atoms, the symmetry type for which a given number of functions is selected should be based on j, not on l, as has been the case in most molecular calculations performed to date.     

Adapted Gaussian basis sets for atoms Cs to Lr based on the generator coordinate Hartree–Fock method

We have applied a discretized version of the generator coordinate Hartree–Fock method to generate adapted Gaussian basis sets for atoms Cs (Z=55) to Lr (Z=103). Our Hartree–Fock total energy results, for all atoms studied, are better than the corresponding Hartree–Fock energy results attained with previous Gaussian basis sets. For the atoms Cs to Lr we have obtained an energy value within the accuracy of 10⁻⁴ to 10⁻³ hartree when compared with the corresponding numerical Hartree–Fock total energy results. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 858–865, 1998     

Uniform quality gaussian basis sets for molecular calculations. III. Charge optimized basis sets

Gradient optimized constrained (2s ≠ 2p) and unconstrained (2s ≠ 2p) Gaussian 3G basis sets are reported for the first-row atoms and ions X^O, for Q = ?2 to +4. Analytic equations have been fitted to the logarithm of the exponents as a function of the nuclear charge Z and formal charge Q. Consequently only two parameters Z and Q have to be specified in order to completely define a basis set.     

Application of an ion-fitted pseudopotential to HF,H2O,NH3, BeO,and HCl in a Gaussian lobe basis

The core potentials for atoms of atomic numer 1–18 fitted to ion spectra by Chang, Habitz, Pittel, and Schwarz have been extended to the molecular case in a Gaussian lobe basis by using a six-Gaussian (6G-POT ) representation for the exponential factors of the atomic core potentials. In a (9s/5p/1d) basis the 6G-POT one-electron energies, dipole moments, and Mulliken charges are improved over a one-Gaussian potential form for HF, NH₃, and H₂O; BeO also yields good agreement within 2.6% of the experimental bond length. For HCl, the core potential shows larger errors in the dipole moment (7%) and one-electron eigenvalues (2%), but a 75% saving in computer time is realized for HCl compared with only about 35% for first-row systems using the 6G-POT core potentials. Analytical expressions are given to extend the 6G-POT method up to s, p, d, f, and g valence shells.     

Modified Gaussian functions and their use in quantum chemistry. I. Integrals

A modified Gaussian function g(u, v, w, a, R ) = const s(a, R ) is considered where l = u + v + w, s (a, R ) is a 1s-type Gaussian function centered at R , a is the coefficient in the exponent of the 1 s Gaussian function and X, Y, Z are components of R . General formulae are derived for overlap integrals, kinetic energy integrals, nuclear attraction integrals, and electron repulsion integrals, valid for any l. The formulae are much simpler than those derived by Huzinaga for Cartesian Gaussian functions.     

Generator coordinate Hartree–Fock method applied to the choice of a contracted Gaussian basis for the second-row atoms

The generator coordinate Hartree–Fock (GCHF) method is employed as a criterion for the selection of a 18s12p Gaussian basis for the atoms Na–Ar. The role of the weight functions in the assessment of the numerical integration range of the GCHF equations is shown. The extended basis is then contracted to (10s6p) by a standard procedure and in combination with the previously contracted (7s5p) Gaussian basis for the atoms Li–Ne is enriched with polarization functions. This basis is tested for AlF, SiO, PN, BCl, and P₂. The properties of interest were HF total energies, MP2 dipolar moments, bond distances, and dissociation energies. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 927–934, 1997     

Copper(II) Chelate Complex with N′-(2,4-Dichlorophenoxy)acetyl-N,N-Dimethylhydrazine: Crystal and Molecular Structure

X-ray diffraction analysis of the copper(II) chelate complex CuL₂ (where L is the deprotonated imid-ol form of N,N-dimethyl-2,4-dichlorophenoxyacetohydrazide (HL)) was performed (3826 reflections, R = 0.039, wR = 0.043). Crystals are monoclinic, a = 8.365(7) Å, b = 23.090(7)Å, c = 12.713(3) Å, = 95.12(6)°, space group P2₁/c, Z = 4. The slightly distorted square environment of the copper cation is composed of two N atoms of the dimethylamino groups and two O atoms of the deprotonated imidol groups. Both N and O atoms are located in trans-positions relative to each other. Additional coordination of electron-donor atoms is prevented by methyl groups, in which the C atoms are at a distance of 2.837 to 2.918 Å from the central ion.     

Accurate relativistic adapted gaussian basis sets for francium through ununoctium without variational prolapse and to be used with both uniform sphere and gaussian nucleus models

Accurate relativistic adapted Gaussian basis sets (RAGBSs) for ₈₇Fr up to ₁₁₈Uuo atoms without variational prolapse were developed here with the use of a polynomial version of the Generator Coordinate Dirac‐Fock method. Two finite nuclear models have been used, the Gaussian and uniform sphere models. The largest RAGBS error, with respect to numerical Dirac‐Fock results, is 15.4 miliHartree for Ununoctium with a basis set size of 33s30p19d14f functions. © 2013 Wiley Periodicals, Inc.     

A new 3s–3d heterometallic polymer containing N‐methyliminodiacetic acid: synthesis,structure and characterization

A new complex {[Na₂(H₂O)₃(µ‐L)₂Cu]₄}_∞ (L = N‐methyliminodiacetic acid) has been synthesized and structurally characterized. The complex crystallizes in the monoclinic, space group C2/c, with the unit cell parameters a = 16.556(3) Å, b = 8.0622(13) Å, c = 12.671(2) Å, α = 90°, β = 95.849(2)°, γ = 90°. The central metal Cu (II) ion is coordinated with two nitrogen atoms and four oxygen atoms belonging to two ligands. Simultaneously, the sodium is six‐coordinated with oxygen atoms coming from the ligand and water molecule; the sodium atoms related are bridged by oxygen atoms, forming a sodium chain. The structure consists of CuL₂ moieties linked by sodium chain via the exo oxygen atoms of two ligands, forming a novel three‐dimensional structure. Moreover, elemental analysis, IR, UV‐vis, ESR spectroscopy and thermal stability were determined. Copyright © 2007 John Wiley & Sons, Ltd.     

Three related benzoannelated diazapolyether macrocycles: effects of macrocycle ring size and position of benzo groups on hydrogen bonding of the amine H atoms

The benzoannelated diazapolyether macrocycles 6,7,9,10,17,18‐hexahydro‐5H,11H‐8,16,19‐trioxa‐5,11‐diazadibenzo[a,g]cyclopentadecene, C₁₈H₂₂N₂O₃, (I), 6,7,9,10,12,13,20,21‐octahydro‐5H,14H‐8,11,19,22‐tetraoxa‐5,14‐diazadibenzo[a,g]cyclooctadecene, C₂₀H₂₆N₂O₄, (II), and 6,7,9,10,17,18,20,21‐octahydro‐16H,22H‐5,8,11,19‐tetraoxa‐16,22‐diazadibenzo[a,j]cyclooctadecene 0.3‐hydrate, C₂₀H₂₆N₂O₄·0.304H₂O, (III), show different patterns of hydrogen bonding. In (I), the amine H atoms participate only in intramolecular hydrogen bonds with ether O atoms. In (II), the amine H atoms form intramolecular hydrogen bonds with the phenoxy ether O atoms and intermolecular hydrogen bonds with alkyl ether O atoms in an adjacent molecule, forming a chain linking the macrocycles together via an R₂²(10) motif. Molecules of (II) were found on a crystallographic twofold axis. In (III), the amine H atoms participate in a hydrogen‐bond network with adjacent ether O atoms and with a water molecule [having a partial occupancy of 0.304 (6)] that links the molecules together via a C₂²(7) motif.     

Multipole expansion of Cartesian Gaussian orbitals about a new origin

Cartesian Gaussian orbitals (CGO) about one center are expanded as a series of spherical harmonics around a new origin. Radial coefficients are given in analytical form. Developments of solid harmonic Gaussian orbitals (SHGO) are also obtained and used to study the convergence properties of expansions of s, p, d, and f Gaussians in terms of a single dimensionless parameter λ. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 647–653, 1997     

Theoretical calculation of the low laying electronic states of the molecular ion KH

Using an ab initio method the potential energy has been calculated for the 25 lowest molecular states of symmetries ²Σ⁺, ²Π, ²Δ for the molecular ion KH⁺. The calculation is based on nonempirical pseudopotentials and parameterized ℓ-dependent polarization potentials. Gaussian basis sets have been used for both atoms. The spectroscopic constants for 18 electronic sates have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance R. Through the canonical functions approach the eigenvalue E_v, the abscissas of the corresponding turning points (R_min and R_max) and the rotational constants B_v have been calculated up to 24 vibrational levels for the considered bound states. The comparison of the present results with those available in literature shows a very good agreement.     

Crystal structure of barium bis [N-(2-hydroxyethyl)iminodiacetato]cobaltate(III) hydrocarbonate dihydrate Ba(μ4-HCO3)[ trans (N)-Co(heida)2]·2H2O

Ba[Co(heida)₂](HCO₃)·2H₂O crystals were grown (orthorhombic, a = 9.4491(5) Å, b = 10.9719(5) Å, c = 19.6077(9) Å, Z = 4, space group Pca2₁), and their structure was solved by X-ray diffraction. The Co atoms in the complex anion were coordinated by two N-(2-hydroxyethyl)iminodiacetate (heida) ligands via the N atom and two O atoms of each ligand. The Ba atoms and the complex anions form “honeycomb” layers linked via three O atoms. The “honeycombs” are additionally linked by their Ba atoms with the O atoms of the hydroxyethyl groups. The Ba atoms are aligned within a layer and linked via the bridging HCO₃ hydrocarbonate groups. The c.n. of Ba atoms is 10 (one water molecule; five O atoms of the complex anions, one from each of the nearest neighbors; and four O atoms of the hydrocarbonate ions). Original Russian Text Copyright ? 2008 by M. Zabel, A. L. Poznyak, and V. I. Pavlovskii __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 49, No. 3, pp. 594–597, May–June, 2008.     

Near-Dirac–Hartree–Fock results for first-row atoms calculated with GTO basis sets

Relativistic basis sets for first-row atoms have been constructed by using the near-Hartree–Fock (nonrelativistic) eigenvectors calculated by Partridge. These bases generate results of near-Dirac–Hartree–Fock quality. Relativistic total and orbital energies, relativistic corrections to the total energy, and magnetic interaction energies for the first-row atoms have been presented. The smallest Gaussian expansions (13s8 p expansions) yield Dirac–Hartree–Fock total energies accurate through six significant digits, while the largest expansions (18s13p expansions) give these energies accurate through seven significant digits. These results are more accurate than some of the results reported earlier, particularly for the open-shell atoms, indicating that the basis employed is reasonably economical for relativistic calculations. © 1995 John Wiley & Sons, Inc.     

Development and testing of a compact basis set for use in effective core potential calculations on rhodium complexes

We present a set of effective core potential (ECP) basis sets for rhodium atoms which are of reasonable size for use in electronic structure calculations. In these ECP basis sets, the Los Alamos ECP is used to simulate the effect of the core electrons while an optimized set of Gaussian functions, which includes polarization and diffuse functions, is used to describe the valence electrons. These basis sets were optimized to reproduce the ionization energy and electron affinity of atomic rhodium. They were also tested by computing the electronic ground state geometry and harmonic frequencies of [Rh(CO)₂μ‐Cl]₂, Rh(CO)₂ClPy, and RhCO (neutral and its positive, and negative ions) as well as the enthalpy of the reaction of [Rh(CO)₂μ‐Cl]₂ with pyridine (Py) to give Rh(CO)₂ClPy, at different levels of theory. Good agreement with experimental values was obtained. Although the number of basis functions used in our ECP basis sets is smaller than those of other ECP basis sets of comparable quality, we show that the newly developed ECP basis sets provide the flexibility and precision required to reproduce a wide range of chemical and physical properties of rhodium compounds. Therefore, we recommend the use of these compact yet accurate ECP basis sets for electronic structure calculations on molecules involving rhodium atoms. © 2012 Wiley Periodicals, Inc.     

Determination of the depth profiles of ion-implanted impurities by electron probe x-ray microanalysis

The aim of this paper is to demonstrate the suitability of electron probe x-ray microanalysis (EPMA) for nondestructive determination of the depth profiles of ion-implanted impurities. The intensities of the characteristic x-ray emission of impurity atoms (P and As) were measured (on a WDX spectrometer) on the implanted specimens and references (GaP and GaAs) at three values of primary electron energy E_P. The range distribution of the implanted impurity as a first approximation is given by a Gaussian distribution. A two-parameter fitting has been developed for the determination of Gaussian parameters R_P and ΔR_P of the profiles, which give a minimal difference between the experimental and calculated x-ray intensities at different E_P. The dose of the implanted impurity is a third parameter that can be obtained here. The results were compared with those of depth profiles from AES (for P) and SIMS (for As) and good agreement is observed. A new method for the determination of the depth distribution of x-ray production for the characteristic x-rays of impurity atoms is also presented.     

Infrared spectra of some isotopomers of isopropylamine: A theoretical study

The normal‐mode frequencies and the corresponding vibrational assignments of some isotopomers of isopropylamine are examined theoretically using the Gaussian 94 set of quantum chemistry codes at the MP2 level of theory using a 6‐311g** basis set. In particular deuteration of the NH₂ hydrogen atoms as well as the deuteration of the CH₃ hydrogen atoms, the α‐CH hydrogen atom, and various combinations of deuteration of isopropylamine are examined. Correction factors for predominant vibrational motions are reported and compared for a number of isotopomers of s‐trans‐ and gauche‐isopropylamine. Comparison of theoretically predicted infrared spectra with experimental spectra is made for isotopomers for which experimental data exist. Enthalpy, entropy, and Gibbs free energy changes are considered for the trans→gauche transformation. An amino torsional potential is deduced and barrier heights are calculated for the trans→gauche, gauche→trans, and gauche→gauche transformations. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 109–126, 1999     

Gaussian expansions from STOs by the distance between subspaces

Expansions of STO orbitals with GTO s for the first-row atoms have been obtained by the method of the distance between subspaces. The expansion coefficients and exponential parameters were simultaneously varied when the distance between subspaces, which are generated from STO and GTO functions, is minimized. The ζ; exponents (or scale factors) for the atomic orbitals that are optimized for these atoms are also shown to be almost independent of the number of Gaussian functions. Comparisons carried out with Stewart's least-squares method produce equivalent results when exponents for 2s and 2p functions are different. Some examples and applications for several atomic properties of the first-row atoms are included: energies and expectation values of rⁱ and pⁱ for the several expansions. These new minimal basis sets were tested for diatomic and polyatomic molecules containing these atoms. © 1993 John Wiley & Sons, Inc.