Orbital localization in transition metal molecules

In multiply bonded, weakly interacting systems the excessive electron repulsion associated with the non-dynamical correlation error can be reduced within the Hartree Fock approximation by localizing the bonding orbitals. The mechanism behind this (unphysical) orbital localization is studied through calculations on a model system, and SCF and CI calculations on the MnO⁺ ion. It is shown, from a pair-population analysis of the two-particle density matrix (which is analogous to a Mulliken population analysis of the one-density) that the orbital localization is a two-electron effect. Transition metal molecules often exhibit this kind of orbital localization which may (or may not) require symmetry breaking. The special characteristics of transition metal molecules that makes them suitable candidates for orbital localization will be discussed.     

Matrix elements for Ĵ2 and Ĵz operators over explicitly correlated Cartesian Gaussian functions

General formalism for evaluation of multiparticle integrals involving J?² and J?_z operators over explicitly correlated Cartesian Gaussian functions is presented. The integrals are expressed in terms of the general overlap integrals. An explicitly correlated Cartesian Gaussian function is a product of spherical orbital Gaussian functions, powers of the Cartesian coordinates of the particle, and exponential Gaussian factors, which depend on interparticular distances. This development is relevant to both adiabatic and nonadiabatic calculations of energy and properties of multiparticle systems. © 1995 John Wiley & Sons, Inc.     

Hylleraas–Configuration Interaction calculations on the 11S ground state of helium atom

Hylleraas–Configuration Interaction (Hy–CI) calculations on the ground 1¹S state of helium atom are presented using s-, p-, d-, and f-Slater orbitals of both real and complex form. Techniques of construction of adapted configurations, optimization of the orbital exponents, and structure of the wave function expansion are explored. A new method to evaluate the two-electron kinetic energy integrals occurring in the Hy–CI method has been tested in this work and compared with other methods. The non-relativistic Hy–CI energy values are ≈10 picohartree accurate, about 2.2 × 10^?6 cm^?1. The Hy–CI calculations are compared with Configuration Interaction (CI) and Hylleraas (Hy) calculations employing the same orbital basis set, same computer code, and same computer machines. The computational required times are reported.     

A study of spiro[indoline-pyridobenzopyrans] by differential pulse voltammetry on a dropping mercury electrode and quantum chemistry

Spiropyrans of the indoline series were studied by differential pulse voltammetry in DMSO solutions. The experimental data obtained were supported by quantum-chemical calculations performed to examine the structural features and thermodynamic stability of a series of spiro-pyrans. The calculations revealed a correlation between the peak potential (E _p) of spiropyrans and the energy of the lowest unoccupied π orbital. Procedures were developed for identification and quantitative determination of all the spiropyrans in DMSO on a mercury dropping electrode in the concentration range from 1 × 10^?7 to 1 × 10^?6 M.     

Accurate density functional calculations on large systems

The theoretical underpinnings of the linear combination of Gaussian-type orbitals (LCGTO ) calculations of the density functional (DF ) energy of molecules and clusters are described. The generating function for three-center integrals of arbitrary angular momenta is given in the solid-spherical-harmonic basis. Variational fitting is described and its accuracy tested. The LCGTO-DF method is used to address questions related to the problem of how it is that the methods of cluster science, i.e., high-energy beams or currents, can be used to make C₆₀ in bulk quantities. In particular, it is shown that C₆₀ is neither especially stable nor is it the only large, stable, perfectly round, approximately sp² carbon molecule. © 1996 John Wiley & Sons, Inc.     

Analytic first derivatives for explicitly correlated,multicenter, Gaussian geminals

Variational calculations utilizing the analytic gradient of explicitly correlated Gaussian molecular integrals are presented for the ground state of the hydrogen molecule. Preliminary results serve to motivate the need for general formulas for analytic first derivatives of molecular integrals involving multicenter, explicitly correlated Gaussian geminals with respect to Gaussian exponents and coordinates of the orbital centers. Explicit formulas for analytic first derivatives of Gaussian functions containing correlation factors of the form exp(-βr_ij²) are derived and discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 991–999, 1997     

半正交化基近似计算的改进

Kashiwagi建议, 在量子化学从头计算中采用半正交化基组, 在电子排斥积分中忽略某些正交轨道间的重迭,同时保留核吸引积分中的类似重迭。本文建议在核吸引积分中也忽略这些微分重迭。这一改进提高了计算的精度。对仍然保留的微分重迭, 在计算三、四中心积分时建议在保持电荷守恒的条件下, 用较简单的轨道对之间的微分重迭代替, 大大节约了计算机时。     

Highly correlated calculations using optimized virtual orbital space with controlled accuracy. Application to counterpoise corrected interaction energy calculations

In this work, we investigate the correlation between error introduced by truncation of optimized virtual orbital space (OVOS) on the MP2 level (Y_MP2) with the error of the post‐MP2 contributions, such as the CCSD‐MP2 (i.e., Y_ΔCCSD), CCSD(T)‐MP2 (i.e., Y_ΔCCSD(T)), or the (T) separately. We found a correlation between the Y_MP2 and several other quantities, such as the percent of recovered optimization functional value in the truncated OVOS (OF%), or the aforementioned Y_ΔCCSD, Y_ΔCCSD(T), Y_(T), which is to good approximation linear in the logarithmic scale. These correlations open a possibility to control the accuracy of the post‐MP2 calculations in the truncated OVOS, because the Y_MP2 and the OF% are easily obtained, almost as a byproduct of the virtual orbital optimization. According to the results present in this work, knowledge of the Y_MP2 or the OF% allows us to safely estimate the order of magnitude of the error of the post‐MP2 corrections. To keep the accuracy of, for instance, CCSD(T) correlation energy calculated in the truncated OVOS within 1.10^?5 ? 1.10^?6 Hartree error bars, we can typically reduce only a few percent of the OVOS, although this value increases slightly with enlarging the atomic orbital (AO) basis set and the number of inactive occupied orbitals. Still, even such a modest reduction can save more then a half of the computation time, compared with calculations in the full VOS. The situation is, however, much more favourable in case of counterpoise (CP) corrected calculations of interaction energy, where this methodology enables safe truncation of significant part of OVOS of monomers, resulting from the presence of the ghost AO. Dimension of such truncated OVOS essentially corresponds to CP‐uncorrected calculations, thus leads to more than an order of magnitude speedup of calculation of monomers. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Semidirect algorithms for third-order electron propagator calculations

An efficient procedure for third-order electron propagator calculations of ionization energies and electron affinities is reported. Diagonal self-energy expressions that are suitable for large molecules are empolyed. The outer-valence Green's function method also is implemented. An integral transformation program for direct and semidirect algorithms is modified to store only nonzero integrals according to Abelian point group symmetry. Contributions to self-energy matrix elements that depend on electron repulsion integrals with four virtual orbital indices are computed in a direct way. Intermediate batches of integrals are created by sort procedures while avoiding storage of transformed integrals in the main memory. This method permits calculation of electron binding energies for C with a 231 atomic orbital basis and for Zn(C₅H₅)₂ with a 220 atomic orbital basis on an IBM RISC/6000 Model 550. During these calculations, the CPU is engaged approximately 90% of the time. © 1995 John Wiley & Sons, Inc.     

Application of cholesky-like matrix decomposition methods to the evaluation of atomic orbital integrals and integral derivatives

When viewed as a square two-indexed matrix, the array of atomic orbital-based, two-electron integrals (ij|kl) is a positive semidefinite array. Beebe and Linderberg showed, in 1977, that actual or near linear dependencies often exist within the types of atomic orbital basis sets employed in conventional quantum chemical calculations. In fact, large (i.e., higher quality) bases were shown to be substantially more redundant than smaller or more spatially separated bases. In situations where there exists significant basis near redundancy, the rank (r) of the (ij|kl) ≡ V_l,J matrix of integrals will be significantly smaller than the matrix dimension M. When this occurs, it proves computationally tractable to decompose the M-dimensional matrix V into components L ( V = LL ^T) which contain all of the information needed to form the full V matrix. The Cholesky algorithm allow such a decomposition to be carried out and forms the basis of the work described here. The method is found to be highly successful in reducing the number of integrals and integral derivatives that must actually be calculated. In particular, results on the C₂ molecule indicate that the algorithm can be superior to traditional methods of integral derivative generation if the orbital basis is large enough to contain appreciable near redundancy. In contrast, results on benzene with a more spatially delocalized basis show that conventional methods are preferred whenever substantial basis (near) redundancy is not present.     

A re-examination of the infrared and ultraviolet spectroscopy of trifluoroacetyl fluoride and trifluoroacetyl chloride: An experimental and theoretical study

The fundamental IR vibrational modes of trifluoroacetyl fluoride CF₃C(O)F and trifluoroacetyl chloride CF₃C(O)Cl have been re-examined by ab initio molecular orbital calculations and compared with literature assignments. Several bands of the IR spectrum are reassigned. The Q-branch and integrated absorption cross-sections have been measured for ν₁, ν₃, ν₄ and ν₁₁ fundamental bands for both pressurized and unpressurized samples on each molecule. The UV absorption spectra of CF₃C(O)F and CF₃C(O)Cl show a structureless continuum with a maximum at 21Onm (σ_max=3.20±0.02 × 10⁻²⁰ cm² molecule⁻¹) and 255 nm (σ_max=7.66±0.26 × 10⁻²⁰ cm² molecule⁻¹), respectively. The nature of the electronic transition giving rise to the UV absorption spectrum for CF₃C(O)F and CF₃C(O)Cl has been examined by ab initio molecular orbital calculations. It is attributed to the A¹A″←X¹A′ electronic transition.     

Tuning of the electronic properties of H‐passivated armchair graphene nanoribbons by mild border oxidation: Theoretical study on periodic models

We report the results of a DFT study of the electronic properties, intended as highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, of periodic models of H‐passivated armchair graphene nanoribbons (a‐GNRs) as that synthetized by bottom‐up technique, functionalized by vicinal dialdehydic groups. This material can be obtained by border oxidation in mild and easy to control conditions with ¹Δ_g O₂ as we reported in our previous paper (Ghigo et al., ChemPhysChem 2015, 16, 3030). The calculations show that the two models of border oxidized a‐GNRs (model A, 0.98 nm and model B, 1.35 nm wide) present LUMO and HOMO energies lowered by an extend roughly linearly dependent on the amount of oxygen chemically bound. The frontier orbital energy variations dependence on the % wt of oxygen bound are, for model A: ?0.12 eV for the LUMO and ?0.05 eV for the HOMO; for model B: ?0.15 eV (HOMO) and ?0.06 eV (LUMO). © 2016 Wiley Periodicals, Inc.     

Multiconfigurational SCF approach for high-symmetry molecules and its applications to fullerene trianion

A symmetry-adapted multiconfiguration self-consistent field (MC SCF) approach aimed at calculations of high-symmetry molecules is proposed. The self-consistency procedure applicable to the molecular terms of any symmetry and multiplicity is developed. It holds the symmetry transformation properties of varied molecular orbitals, thus taking advantage of the relationships within the set of two-electron integrals through molecular invariants. For orbital optimization, a unified coupling operator is constructed on the basis of the pseudosecular method providing for efficient convergence to energy minimum. Based on the group-theory technique, computer codes have been developed for straightforward determination of the invariant expansions for two-electron integrals and configuration interaction (CI) matrix elements. Calculated in this way, the expansion coefficients are presented for the three-electron states that originate from joint t_1u and t_1g shells of an icosahedral fullerene C₆₀, the case important for the calculations of anion C₆₀³⁻ representing the charge state of the fullerene molecule in the superconducting ionic solids K₃C₆₀ or Rb₃C₆₀. The results of MC SCF calculations for lowest quasi-π-electronic states of C₆₀³⁻ are discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 293–304, 1998     

On an IC electronic balance control system and its impact on the calibration

The contribution deals with an “1974 integrated circuit” version of an electronic damping and nulling system, adapted to a torsion balance which now is more than twenty years old. The discussion of calibration results reveal that masses of about 0.5 mg, in certain cases, can be intercompared with a relative precision of 3 × 10^?5, indicating that the balance sensibility is better than 2 × 10^?8 g. As the deflection sensitivity of the balance is 1.3 × 10^?4 deg/μg the position sensor on the balance can detect, over a few minutes, average displacements of about 4 × 10^?7 cm (i.e. ～ 40 Å).     

Quantum efficiency of the 2537 A. Photolysis of a mixed phenyl–methyl polysiloxane

The ultraviolet (λ = 2537 A.) photolysis of a degassed mixed phenyl and methyl polysiloxane liquid is examined in terms of gas and crosslinking yields. Results are compared to the published values obtained by ionizing irradiation of this type of molecule. It is shown that ultraviolet radiation is less efficient by two orders of magnitude in producing decomposition (i.e., gaseous products) than is ionizing radiation. The comparisons for crosslinking efficiencies are less certain, but the yields seem to have much more similar values in this case based on a spectroscopic estimation of crosslinking (i.e., analysis for substituted phenylcyclohexadiene formation). The gas quantum yields were ?H₂ = 2.6 × 10^?5, ?CH₄ = 0.63 × 10^?5, ?C₂H₆ ≈ 0.12 × 10^?5, and ?C₂H₂ ≈ 0.06 × 10^?5.     

Use of polymethine dyes for the extraction separation and spectrophotometric determination of nitrophenols

The extraction of nitrophenols with polymethine dyes of the common formula R₁-(CH=CH)₃-R₂, indolium and benzothiazolium derivatives was studied. The effect of the acidity of the solution, the nature and the concentration of the dye, and the nature of the organic solvent on the formation and extraction of ion pairs of nitrophenols was examined; the optimum conditions were found. The most important chemical analytical characteristics of the ion pairs were determined. Molar absorptivities of extracts are 11.9 × 10⁴–14.3 × 10⁴ for ion pairs of trinitrophenol and 6.8 × 10⁴–10.1 × 10⁴ for ion pairs of dinitrophenol. A new procedure was developed for the extraction-photometric determination of nitrophenols in a mixture.     

Molecular orbital studies on small molecules using H2+-type elliptical basis orbitals. Application to H2+, H2, He2++ and H3+

H₂⁺-type elliptical orbitals are defined in Section 1. These orbitals, which in elliptical coordinates involve a factor (1 + ξ)^σ, are employed in variational calculations on the ground states of H₂⁺ and H₂ (Sections 2 and 3). Various choices of σ are explored for H₂⁺, while two choices are used for H₂ : the “boundary condition” (Equation 6) and the “cusp condition” (Equation 9) values. Variational energies are calculated and compared to the results of similar calculations. Section 3 concludes by employing the H₂⁺-type orbitals in LCETO-MO-SCF calculations on the ground states of H₂ and He₂⁺⁺. For both molecules a four-function basis set with two (nonlinear) variational parameters yields more than 99% of the Hartree-Fock limit. Section 4 deals with LCETO-MO-SCF calculations on triangular H₃⁺. Three four-function basis sets are used, and the best energy is -1.2306 a.u., which is in reasonable agreement with the Hartree-Fock limit, -1.2999 a.u. Our best basis set is a four-term two-center expansion of the wave function with only one nonlinear variational parameter. Section 5 concludes the paper with a summary of the methods used to evaluate the integrals which arise in SCF calculations in the H₂⁺-type elliptical orbital basis.     

Theoretical studies on ferromagnetic behavior of [Cr(C5(CH3)5)2]+[TCNE]− and [Mn(C5(CH3)5)2]+[TCNQ]−

By using broken-symmetry hybrid-DFT (UB3LYP and UB2LYP) calculation, the effective exchange integrals (J values) of [Cr(C₅(CH₃)₅)₂]⁺[TCNE]⁻[Cr(C₅(CH₃)₅)₂]⁺ and [Mn(C₅(CH₃)₅)₂]⁺[TCNQ]⁻[Mn(C₅(CH₃)₅)₂]⁺ were determined theoretically. Those calculated models were reduced to 3-spin-sites models from X-ray crystallographic data of charge transfer 3D crystal. The calculated results showed that effective exchange integrals were positive and the signs of spin densities on the cyclopentadienyl rings were negative. These results supported the so-called McConnell I mechanism for ferromagnetism proposed by Kollmar et al. and our previous calculations. Natural orbital analysis made it clear that the orbital overlap between SOMO on metals and SOMO on TCNE or TCNQ cations was nearly zero. These results indicated that orbital orthogonality was an important key factor for explaining the ferromagnetism of those systems.     

Electric and magnetic multipole integrals in STO basis sets: an analytical approach

A new method for the evaluation of one- and two-centre magnetic and electric multipole integrals for Slater-type functions is presented. The method is strictly analytical in that no approximations of any kind are involved. Two simple functions, ℐ₁ ^aug and ℐ₂ ^aug, are introduced, which employ only functions that are well known in electronic structure theory. With the use of augmentation exponents these functions apply to multipole integrals as well as other one-electron integrals, such as nuclear attraction integrals. The proposed method includes the analytic determination of derivatives of the integrals with respect to atomic displacements. Some illustrative test calculations are presented and compared to results from the literature. Received: 20 April 1998 / Accepted: 13 October 1998 / Published online: 1 February 1999