On the use of local basis sets for localized molecular orbitals

Two procedures are discussed for the direct variational optimization of localized molecular orbitals which are expanded in local subsets of the molecular basis set. It is shown that a Newton-Raphson approach is more efficient than an iterative diagonalization scheme. The effect of the basis-set truncation on the quality ofab-initio SCF results is investigated for Be, Li₂, HF, H₂O, NH₃, CH₄ and C₂H₆.     

Analogy between real irreducible tensor operator and molecular two-particle operator

. Molecular matrix elements of a physical operator are expanded in terms of polycentric matrix elements in the atomic basis by multiplying each by a geometrical factor. The number of terms in the expansion can be minimized by using molecular symmetry. We have shown that irreducible tensor operators can be used to imitate the actual physical operators. The matrix elements of irreducible tensor operators are easily computed by choosing rational irreducible tensor operators and irreducible bases. A set of geometrical factors generated from the expansion of the matrix elements of irreducible tensor operator can be transferred to the expansion of the matrix elements of the physical operator to compute the molecular matrix elements of the physical operator. Two scalar product operators are employed to simulate molecular two-particle operators. Thus two equivalent approaches to generating the geometrical factors are provided, where real irreducible tensor sets with real bases are used. Received: 3 September 1996 / Accepted: 19 December 1996     

Complete graph conjecture for inner-core electrons: homogeneous index case

The complete graph conjecture that encodes the inner-core electrons of atoms with principal quantum number n >or= 2 with complete graphs, and especially with odd complete graphs, is discussed. This conjecture is used to derive new values for the molecular connectivity and pseudoconnectivity basis indices of hydrogen-suppressed chemical pseudographs. For atoms with n = 2 the new values derived with this conjecture are coincident with the old ones. The modeling ability of the new homogeneous basis indices, and of the higher-order terms, is tested and compared with previous modeling studies, which are centered on basis indices that are either based on quantum concepts or partially based on this new conjecture for the inner-core electrons. Two similar algorithms have been proposed with this conjecture, and they parallel the two "quantum" algorithms put forward by molecular connectivity for atoms with n > 2. Nine properties of five classes of compounds have been tested: the molecular polarizabilities of a class of organic compounds, the dipole moment, molar refraction, boiling points, ionization energies, and parachor of a series of halomethanes, the lattice enthalpy of metal halides, the rates of hydrogen abstraction of chlorofluorocarbons, and the pED(50) of phenylalkylamines. The two tested algorithms based on the odd complete graph conjecture give rise to a highly interesting model of the nine properties, and three of them can even be modeled by the same set of basis indices. Interesting is the role of some basis indices all along the model.     

Complete basis set ab initio computational study of ionization potential, electron affinity and the C-F bond dissociation energy for perfluorinated methane derivatives

A computational study of perfluorinated methane derivatives was performed with complete basis set ab initio methods. The total energies for their neutral, cation, and anionic states were computed. From these values, the energy gaps between different electronic states, ionization potentials, electron affinities, and C-F bond dissociation energies were calculated. The computed values are compared with experimental data and the reliability of complete basis set ab initio methods is discussed. New values for C-F bond dissociation energies are suggested. Received: 12 January 1998 / Accepted: 2 April 1998 / Published online: 29 July 1998     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of BiH₃ (–0.499 a.u.), PoH₂ (–0.207 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to —0.230 a.u., –0.177 a.u., and –0.097 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system.     

Ab initio and DFT studies on hydrolyses of phosphorus halides

Hydrolyses of phosphorus halides, (RO)(2)POX where R = H or Me and X = F or Cl, in the gas phase and in the reaction field have been investigated theoretically with ab initio and the density functional theory (DFT). The free energy of activation in the reaction field was also estimated using the Onsager method with a correction of entropy change and basis set superposition error (BSSE). The reaction of (MeO)(2)POF proceeds through a path with bifunctional catalysis regardless of the medium, but the reaction of (MeO)(2)POCl proceeds through bifunctional and general base catalysis in the gas phase and in water, respectively. The estimated free energy barrier of 23 kcal/mol for the hydrolysis of (MeO)(2)POF is in good agreement with the experimental values of 24 kcal/mol, and relative barrier of 3 kcal/mol to the (MeO)(2)POCl is also in good agreement with the experimental values of 5 kcal/mol of diisopropyl phosphorus halides ((Pr(i)O)(2)POX, X = F and Cl).     

X-H (X = C, N, O, Si, P, S) 键离解能计算的密度泛函方法研究

使用了不同密度泛函方法计算X-H (X = C, N, O, Si, P, S) 键离解能，并分析不同密度泛函方法的计算精度。研究发现大多数密度泛函方法包括B3LYP, B3P86, B3PW91, G96LYP, PBE1PBE，和BH&HLYP都明显低估键离解能13-25 kJ/mol。该现象与是否使用无限基组无关，因为即使使用无限基组键离解能仍然被低估。因此密度泛函方法不适合用于键离解能的估算。其中B3P86方法的偏差最小。进一步分析表明，使用限制性开壳层计算并无任何优势，在大多数情况下非限制性开壳层计算实际上比限制性开壳层计算要好。最后，我们发现了密度泛函方法对键离解能的低估是系统的，因此建议利用校准后的UDFT/6-311++G(d, p)方法计算化学键离解能。     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

A characterization of nonreflexive banach spaces

D. P. Mil'man and V. D. Mil'man considered sequences of decreasing nonempty closed bounded convex sets with empty intersection to obtain characteristics of non-reflexivity. They showed that in every nonreflexive space there is such a sequence which is ω-separated. We show that in every nonreflexive space there is also always such a sequence which is not ω-separated