Ab initio calculations on sulfur-containing compounds. II. One-electron properties of H2S

Closed-shell RHF one-electron properties are calculated for H₂S using a total of 41 different s, p basis sets and two polarized basis sets (6–31G* and 6–31G**). Total energies and geometries alone are not a comprehensive criteria for selecting the best basis sets. It is shown here that the comparison of a number of one-electron properties can serve as an excellent criteria for testing basis sets. The quality or reliability of a basis set is taken as being its agreement with a large uncontracted s, p basis set (s, p limit).     

Compact contracted basis sets for third-row atoms: Ga–Kr

The (14s11p5d) primitive basis set of Dunning for the third-row main group atoms Ga-Kr has been contracted [6s4p1d]. The core functions have been relatively highly contracted while those which represent the valence region have been left uncontracted to maintain flexibility. Calculations with the [6s4p1d] contraction are reported for a variety of molecules involving third-row atoms. This basis set is found to satisfactorily reproduce experimental properties such as geometric configurations, dipole moments, and vibrational frequencies for a range of molecules. Comparisons are made with the performance of the uncontracted basis set. Polarization functions for the contracted basis set are reported and performance of the basis set with and without polarization functions is examined. A relaxation of the [6s4p1d] contraction to [9s6p2d] for higher level evergy calculations is also presented.     

Core polarization and relativistic effects competition in the first ionization potentials for some systems in the Cu,Ag, and Au isoelectronic sequences

Single-configuration relativistic Hartree–Fock values of the first ionization potentials for Cu through Kr⁷⁺, Ag through I⁶⁺, and Au through Pb³⁺ are computed in “frozen” and “relaxed core” approximations with and without allowance for core polarization. Effects of polarization of the atomic core by the valence electron are included by introducing a polarization potential in the one-electron Hamiltonian of the valence electron. The core polarization potential depends on two parameters, the static dipole polarizability of the core α and the cut-off radius r₀, which are chosen independently of the ionization potential data. It is demonstrated that by including the core polarization potential with α and r₀ parameters, which are simply chosen instead of being empirically fitted, it is still possible to account, on the average, for at least 70% of the discrepancy between the single-configuration relativistic Hartree–Fock ionization potentials and the experiment, a discrepancy usually ascribed to the contribution of valence-core electron correlations, and to bring the theoretical ionization potentials to an average agreement with experiment of around 1%. It can be concluded from this study that for low and medium Z elements the core polarization dominates for neutral systems or systems in low ionization stages, whereas for highly ionized systems the relativistic effects prevail. For heavy elements, however, the core polarization influence is comparable to the relativistic one only for neutral systems, whereas for ions the relativistic effects are overwhelmingly predominant.     

Applications of ESCA to polymer chemistry. XVII. Systematic investigation of the core levels of simple homopolymers

The core levels of a series of 83 homopolymers have been studied by electron spectroscopy for chemical analysis (ESCA). Comparisons of the experimentally determined core-level binding energies with theoretical calculations using the ground-state potential model in the complete neglect of differential overlap (CNDO/2) self-consistent field molecular orbital (SCF MO) formalism have been made on the C_1s and O_1s core levels for the oxygen-containing polymers in the series. A comparison of the ground-state potential model (GPM) and relaxation potential model (RPM) on a series of six model compounds representative on the series of polymers is given. Compilations are given of binding energies of C_1s, O_1s, N_1s, Cl_2p, S_2p, Si_2p, and Br_3d levels for typical structural features of common occurrence in polymer systems. These data, taken in conjunction with that previously published on fluoropolymers, provide a sound basis for the development of ESCA as a fingerprint tool in the elaboration of features of structure and bonding in polymers in general.     

A theoretical determination of the dissociation energy of the nitric oxide dimer

Summary Multi-reference CI methods have been applied to determine the dissociation energy and structure of thecis-N₂O₂ molecule. The convergence of the theoretical result has been checked with respect to a systematic expansion of the one-electron basis set and the multi-reference CI wave function. The best calculated value, 13.8 kJ/mol, is in agreement with the experimental value, 12.2 kJ/mol. It has been obtained with an extended ANO-type basis set [6s5p3d2f], including the effect of the basis set superposition error (BSSE) in the geometry optimization, and additional effects, such as the electron correlation of core electrons and relativistic corrections, using the average coupled pair functional (ACPF) approach. The optimal geometry computed at this level was found to be:r(NN)=2.284 Å,r(NO)=1.149 Å, and s5p3d2f] basis set, the BSSE was found to be 2 kJ/mol.     

Anab initio potential energy surface and dynamics calculations for vibrational excitation of I2 by He

We present newab initio calculations of the interaction potential and the elastic and inelastic cross sections for He scattering by I₂. The electronic structure calculations of the interaction potential are based on an extensive one-electron basis set (triple zeta plus ad set on each I, ans function plus ap set at the I₂ bond center, and quadruple zeta plus twop sets on He), a two-configuration-SCF orbital set, and a configuration interaction calculation based on all single and double excitations out of the two-configuration reference space. The calculations are performed at 16He-I₂ distances for nine combinations of I₂ vibrational displacement and orientation. A new form of analytic representation is presented that is particularly well suited to efficient and accurate fitting ofab initio interaction potentials that include vibrational displacements. Scattering calculations are performed by the vibrational close-coupling, rotational-infinite-order-sudden approximation with a converged vibrational basis.     

Theoretical study of low‐lying electronic states of the LiRb+ molecular ion: Structure,spectroscopy and transition dipole moments

The electronic structure and the spectroscopic properties for low‐lying electronic states of the LiRb⁺ molecular ion, dissociating into Li (2s, 2p, 3s, 3p, 3d, 4s, and 4p) + Rb⁺ and Li⁺ + Rb (5s, 5p, 4d, 6s, 6p, 5d, and 7s), have been investigated using an ab initio approach based on non‐empirical pseudo potentials for the Li and Rb cores and parametrized l‐dependent polarization potential. We have determined the adiabatic potential energy curves and their spectroscopic constants for many electronic states of ²Σ⁺, ²Π, and ²Δ symmetries. A satisfying agreement, for the spectroscopic constants, has been obtained for the ground and the first excited states with the available theoretical works. Potential energy curves were presented, for the first time, for the higher excited states. In addition, we have localised and analysed the avoided crossings between electronic states of ²Σ⁺ and ²Π symmetries. Their existences can be related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Li⁺Rb and LiRb⁺. Moreover, we have determined the transition dipole moments from X²Σ⁺ and 2²Σ⁺ states to higher excited states of ²Σ⁺ and ²Π symmetries. For our best knowledge, no experimental data on the LiRb⁺ molecular ion is available. These theoretical data can help experimentalists to optimize photoassociative formation of ultracold LiRb⁺ molecular ion and their longevity in a trap or in an optical lattice. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

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.     

An ab initio molecular orbital study of the structures and energies of neutral and charged bimolecular complexes of NH3 with the hydrides AHn (A = N,O, F,P, S,and Cl)

Hartree-Fock 6-31G(d) structures for the neutral, positive ion, and negative ion bimolecular complexes of NH₃ with the first- and second-row hydrides AH_n (AH_n = NH₃, OH₂, FH, PH₃, SH₂, and ClH) have been determined. All of the stable neutral complexes except (NH₃)₂, the positive ion complexes with NH₃ as the proton acceptor, and the negative ion complexes containing first-row anions exhibit conventional hydrogen bonded structures with essentially linear hydrogen bonds and directed lone pairs of electrons. The positive ion complex NH₄⁺ …? OH₂ has the dipole moment vector of H₂O instead of a lone pair directed along the intermolecular line, while the complexes of NH₄⁺ with SH₂, FH, and ClH have structures intermediate between the lone-pair directed and dipole directed forms. The negative ion complexes containing second-row anions have nonlinear hydrogen bonds. The addition of diffuse functions on nonhydrogen atoms to the valence double-split plus polarization 6-31G(d,p) basis set usually decreases the computed stabilization energies of these complexes. Splitting d polarization functions usually destabilizes these complexes, whereas splitting p polarization functions either has no effect or leads to stabilization. The overall effect of augmenting the 6-31G(d,p) basis set with diffuse functions on nonhydrogen atoms and two sets of polarization functions is to lower computed stabilization energies. Electron correlation stabilizes all of these complexes. The second-order Møller–Plesset correlation term is the largest term and always has a stabilizing effect, whereas the third and fourth-order terms are smaller and often of opposite sign. The recommended level of theory for computing the stabilization energies of these complexes is MP2/6-31+G(2d,2p), although MP2/6-31+G(d,p) is appropriate for the negative ion complexes.     

Ionic bonding of lanthanides,as influenced by d‐ and f‐atomic orbitals,by core–shells and by relativity

Lanthanide trihalide molecules LnX₃ (X = F, Cl, Br, I) were quantum chemically investigated, in particular detail for Ln = Lu (lutetium). We applied density functional theory (DFT) at the nonrelativistic and scalar and SO‐coupled relativistic levels, and also the ab initio coupled cluster approach. The chemically active electron shells of the lanthanide atoms comprise the 5d and 6s (and 6p) valence atomic orbitals (AO) and also the filled inner 4f semivalence and outer 5p semicore shells. Four different frozen‐core approximations for Lu were compared: the (1s²–4d¹⁰) [Pd] medium core, the [Pd+5s²5p⁶ = Xe] and [Pd+4f¹⁴] large cores, and the [Pd+4f¹⁴+5s²5p⁶] very large core. The errors of Lu? X bonding are more serious on freezing the 5p⁶ shell than the 4f¹⁴ shell, more serious upon core‐freezing than on the effective‐core‐potential approximation. The Ln? X distances correlate linearly with the AO radii of the ionic outer shells, Ln³⁺‐5p⁶ and X^?‐np⁶, characteristic for dominantly ionic Ln³⁺‐X^? binding. The heavier halogen atoms also bind covalently with the Ln‐5d shell. Scalar relativistic effects contract and destabilize the Lu? X bonds, spin orbit coupling hardly affects the geometries but the bond energies, owing to SO effects in the free atoms. The relativistic changes of bond energy BE, bond length R_e, bond force k, and bond stretching frequency v_s do not follow the simple rules of Badger and Gordy (R_e～BE～k～v_s). The so‐called degeneracy‐driven covalence, meaning strong mixing of accidentally near‐degenerate, nearly nonoverlapping AOs without BE contribution is critically discussed. © 2015 Wiley Periodicals, Inc.     

Structural and electronic properties of PbZrxTi1‐xO3 (x = 0.5, 0.375): A quantum chemical study

The structural and electronic properties of the PZT materials PbZr_0.5Ti_0.5O₃ and PbZr_0.375Ti_0.625O₃ were studied by means of a Hartree–Fock quantum chemical semiempirical method that employs a periodic large unit cell (LUC) model. The atomic relaxation observed upon introduction of the Zr impurities resulted in outward oxygen atom displacements along the 〈100〉 direction for the cubic phases and varied oxygen and lead atom movements for the tetragonal structures. For these materials, the conduction bands (CB) were composed mainly of Pb 6p atomic orbitals with less important contributions of Zr 4d and Ti 3d states. The upper valence band (UVB) for the cubic phases was mostly Pb 6s in nature, with minor contribution of O 2p atomic orbitals. The tetragonal phase on the other hand was formed by Pb 6s with some contribution of admixed O 2p with Zr s atomic orbitals. The optical band gap (ΔSCF method) was found to decrease going from the cubic to the tetragonal phase in both titanates. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 95: 37–43, 2003     

Static electric properties of LiH: explicitly correlated coupled cluster calculations

Explicitly correlated MBPT-R12 and coupled cluster [up to CCSD(T)-R12] methods have been used in calculations of various (vibrationless) electrical properties for the LiH molecule, including the dipole and quadrupole moments, dipole and quadrupole polarizability tensors, dipole hyperpolarizability tensors, and the second dipole hyperpolarizability tensors. Generally, with extension of the basis set the R12 method did not lead to faster convergence for the calculated properties towards the basis limit. Nevertheless, R12 calculations serve as useful indicators to judge the reliability of the results, and substantially help in determining the accuracy. Results obtained with the 11s8p6d5f/9s8p6d5f basis and CCSD(T)-R12 calculated within this work should be close to the basis set limit. Received: 8 June 1998 / Accepted: 23 July 1998 / Published online: 7 October 1998     

Theoretical studies of organometallic compounds. II. All electron and pseudopotential calculations of M(CH3)nCl4 − n (M = C,Si, Ge,Sn, Pb; n = 0–4)

The performance of effective core potentials (ECP) for the main group elements of group IV has been studied by calculating the geometries and reaction energies of isodesmic reactions for the molecules M(CH₃)_nCl_{4 ? n} (M = C, Si, Ge, Sn, Pb; n = 0–4) at the Hartree–Fock level of theory. The results are compared with data from all electron calculations and experimental results as far as available. The all electron calculations were performed with a 3-21G(d) and a 6-31G(d) basis set for Si, a (43321/4321/41) basis set for Ge, and a (433321/43321/431) basis set for Sn. For the ECP calculations the potentials developed by Hay and Wadt with a configuration (n)s^a(n)p^b and the valence basis set (21/21), extended by a set of d functions, are employed. © 1992 by John Wiley & Sons, Inc.     

High-quality Gaussian basis sets for fourth-row atoms

Summary Energy-optimized Gaussian basis sets of triple-zeta quality for the atoms Rb-Xe have been derived. Two series of basis sets are developed; (24s 16p 10d) and (26s 16p 10d) sets which we expand to 13d and 19p functions as the 4d and 5p shells become occupied. For the atoms lighter than Cd, the (24s 16p 10d) sets with triple-zeta valence distributions are higher in energy than the corresponding double-zeta distribution. To ensure a triple-zeta distribution and a global energy minimum the (26s 16p 10d) sets were derived. Total atomic energies from the largest basis sets are between 198 and 284E _H above the numerical Hartree-Fock energies.     

Contraction of the well-tempered Gaussian basis sets: The first-row diatomic molecules

The well-tempered Gaussian basis sets (14s 10p) for atoms from lithium to neon were contracted and used in restricted Hartree–Fock calculations on 13 systems: Li₂(Σ), B₂(Σ), C₂(Σ), N₂(Σ), O₂(Σ), F₂(Σ), Ne₂(Σ), LiF(Σ), BeO(Σ), BF(Σ), CN^?(Σ), CO(Σ), and NO⁺(Σ). Spectroscopic constants (R_e, ω_e, ω_ex_e, B_e, α_e, and k_e) and one-electron properties (dipole, quadrupole, and octupole moments at the center of mass and electric field, electric field gradient, potential, and electron density at the nuclei) were evaluated and compared with the Hartree–Fock results. The largest contracted basis set (7_s6_p3_d) gives results very close to the Hartree–Fock values; the remaining differences are attributed to the absence of the f functions in the present basis sets. For Ne₂, the interaction energy was calculated; the magnitude of the basis-set superposition error was found to be very small (less than 3 μE_h at 2.8 a₀ and less than 2 μE_h at 5.0 a₀).     

Ionization potential of excited states of Be‐like sequence in the concept of iso‐spectrum‐level series

With the introduction of the concept of the iso‐spectrum‐level series, a linear relationship is found between the first differences of the ionization potential of excited states and nuclear charge Z along an iso‐spectrum‐level series, and the ionization potential of excited states of Be‐like sequence are studied systematically on the basis of the weakest bound electron potential model theory. The expression of nonrelativistic ionization potential is derived from the weakest bound electron potential model theory, and relativistic effects are included by using a fourth‐order polynomial in Z. As a demonstration, the ionization potentials of [He]2s2p ³P, [He]2s3s ¹S₀, [He]2s3p ¹P, [He]2s3d ¹D₂, and [He]2s4d ¹D₂ series for a range of Be‐like sequence from Z = 4–23 are calculated. The results are compared with the experimental data and the recent sophisticated ab initio results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 344–350, 2003     

Studies of Fe2(CO)9 Formation in the Thermolysis of Fe(CO)5 Using Ab Initio Calculations of Fe(CO)5 and Fe(CO)4

Ab initio calculations using the GAMESS program package in the atomic basis TZV (Fe: (14s, 11p, 6d)/[10s, 8p, 3d]; C, O: (11s, 6p)/[5s, 3p]) were performed with account taken of the correlation with the second-order Möller–Plesset (MP2) perturbation theory to predict a new conformer Fe(CO)₄ (with D _4h symmetry). This conformer has a square planar configuration in the ground singlet electronic state and is a mild electrophile produced by dissociation of Fe(CO)₅ along the axial Fe–C bond. The process of nucleation of iron nanoparticles Fe(CO)₅ + Fe(CO)₄ Fe₂(CO)₉ is supposed to occur in two stages. The first stage is an orbital-controlled reaction which should be monitored as an increase in medium polarity and temperature. It should proceed with participation of only one of the stable conformers of the nucleophile Fe(CO)₅, namely, a mild conformer with square-pyramidal structure (C _4v ) rather than a hard but energetically more advantageous conformer with trigonal–bipyramidal structure (D _3h ). The structure of a prereaction complex was discussed.     

Laser and radiofrequency spectroscopy of the 5d 4 6s 6 D multiplet in Ta I

The hyperfine structure (hfs) of¹⁸¹Ta has been investigated using laser radio-frequency double resonance and high resolution laser spectroscopy on collimated atomic beams. The magnetic dipole and electric quadrupole hyperfine structure coupling constants of the 5d ^{4 6} s 6D _{3/2, 5/2, 7/2, 9/2} metastable states have been determined using radio-frequency spectroscopy. In the 5d ⁴ 6s ⁶ D _1/2 metastable state and the excited 5d ³ 6s 6p ⁴ D _3/2,⁶ D _{5/2, 9/2} as well as the unidentified 28 182.6 cm^–1 and 30 021.2 cm^–1 states, hfs constants have been obtained from high resolution laser spectroscopy. A radio-frequency converter has been developed in order to reach the frequency region 2.7–10 GHz.