Communications on quantum similarity,part 3: A geometric‐quantum similarity molecular superposition algorithm

This work describes a new procedure to obtain optimal molecular superposition based on quantum similarity (QS): the geometric‐quantum similarity molecular superposition (GQSMS) algorithm. It has been inspired by the QS Aufbau principle, already described in a previous work, to build up coherently quantum similarity matrices (QSMs). The cornerstone of the present superposition technique relies upon the fact that quantum similarity integrals (QSIs), defined using a GTO basis set, depend on the squared intermolecular atomic distances. The resulting QSM structure, constructed under the GQSMS algorithm, becomes not only optimal in terms of its QSI elements but can also be arranged to produce a positive definite matrix global structure. Kruskal minimum spanning trees are also discussed as a device to order molecular sets described in turn by means of QSM. Besides the main subject of this work, focused on MS and QS, other practical considerations are also included in this study: essentially the use of elementary Jacobi rotations as QSM refinement tools and inward functions as QSM scaling methods. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Subshell fitting of relativistic atomic core electron densities for use in QTAIM analyses of ECP-based wave functions

Scalar-relativistic, all-electron density functional theory (DFT) calculations were done for free, neutral atoms of all elements of the periodic table using the universal Gaussian basis set. Each core, closed-subshell contribution to a total atomic electron density distribution was separately fitted to a spherical electron density function: a linear combination of s-type Gaussian functions. The resulting core subshell electron densities are useful for systematically and compactly approximating total core electron densities of atoms in molecules, for any atomic core defined in terms of closed subshells. When used to augment the electron density from a wave function based on a calculation using effective core potentials (ECPs) in the Hamiltonian, the atomic core electron densities are sufficient to restore the otherwise-absent electron density maxima at the nuclear positions and eliminate spurious critical points in the neighborhood of the atom, thus enabling quantum theory of atoms in molecules (QTAIM) analyses to be done in the neighborhoods of atoms for which ECPs were used. Comparison of results from QTAIM analyses with all-electron, relativistic and nonrelativistic molecular wave functions validates the use of the atomic core electron densities for augmenting electron densities from ECP-based wave functions. For an atom in a molecule for which a small-core or medium-core ECPs is used, simply representing the core using a simplistic, tightly localized electron density function is actually sufficient to obtain a correct electron density topology and perform QTAIM analyses to obtain at least semiquantitatively meaningful results, but this is often not true when a large-core ECP is used. Comparison of QTAIM results from augmenting ECP-based molecular wave functions with the realistic atomic core electron densities presented here versus augmenting with the limiting case of tight core densities may be useful for diagnosing the reliability of large-core ECP models in particular cases. For molecules containing atoms of any elements of the periodic table, the production of extended wave function files that include the appropriate atomic core densities for ECP-based calculations, and the use of these wave functions for QTAIM analyses, has been automated.     

EMP as a similarity measure: a geometric point of view

Soft Coulomb potentials constructed by multiplying the classical potential by a Gaussian function (or a linear combination of them) permit to consider a wide family of distributions which limit with the classical potential when the exponent becomes infinite. Soft Coulomb potentials can be employed as potential operators with first order density functions in order to compute families of soft electrostatic molecular potentials (EMP) for any quantum object. The soft EMP family possesses two interesting computational features: being not only formally equivalent to classical EMP, but finite everywhere, even at the atomic nuclei. The structure of the soft Coulomb operator family yielding soft EMP can be easily related with a quantum similarity integral feature.     

On the basis‐set dependence of local and integrated electron density properties: Application of a new computer program for quantum‐chemical density analysis

A new computer program for post‐processing analysis of quantum‐chemical electron densities is described. The code can work with Slater‐ and Gaussian‐type basis functions of arbitrary angular momentum. It has been applied to explore the basis‐set dependence of the electron density and its Laplacian in terms of local and integrated topological properties. Our analysis, including Gaussian/Slater basis sets up to sextuple/quadruple‐zeta order, shows that these properties considerably depend on the choice of type and number of primitives utilized in the wavefunction expansion. Basis sets with high angular momentum (l = 5 or l = 6) are necessary to achieve convergence for local properties of the density and the Laplacian. In agreement with previous studies, atomic charges defined within Bader's Quantum Theory of Atoms in Molecules appear to be much more basis‐set dependent than the Hirshfeld's stockholder charges. The former ones converge only at the quadruple‐zeta/higher level with Gaussian/Slater functions. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Molecular electronic density fitting using elementary Jacobi rotations under atomic shell approximation

Fitted electron density functions constitute an important step in quantum similarity studies. This fact not only is presented in the published papers concerning quantum similarity measures (QSM), but also can be associated with the success of the developed fitting algorithms. As has been demonstrated in previous work, electronic density can be accurately fitted using the atomic shell approximation (ASA). This methodology expresses electron density functions as a linear combination of spherical functions, with the constraint that expansion coefficients must be positive definite, to preserve the statistical meaning of the density function as a probability distribution. Recently, an algorithm based on the elementary Jacobi rotations (EJR) technique was proven as an efficient electron density fitting procedure. In the preceding studies, the EJR algorithm was employed to fit atomic density functions, and subsequently molecular electron density was built in a promolecular way as a simple sum of atomic densities. Following previously established computational developments, in this paper the fitting methodology is applied to molecular systems. Although the promolecular approach is sufficiently accurate for quantum QSPR studies, some molecular properties, such as electrostatic potentials, cannot be described using such a level of approximation. The purpose of the present contribution is to demonstrate that using the promolecular ASA density function as the starting point, it is possible to fit ASA-type functions easily to the ab initio molecular electron density. A comparative study of promolecular and molecular ASA density functions for a large set of molecules using a fitted 6-311G atomic basis set is presented, and some application examples are also discussed.     

Reduced basis set for the gold atom in cluster complexes

To extend the metal cluster size used in interfacing between bulk metals and molecules in ab initio studies of molecular electronics and chemisorption, a reduced size atomic orbital basis set for the gold atom has been generated. Based on the SKBJ relativistic effective core potential set, the three component 5d Gaussian orbital basis set is completely contracted. Comparisons between the full and reduced basis set in Au atom clusters and cluster complexes for geometry, bond distances, dipole moments, atomic charges, spin, bond dissociation energies, lowest energy harmonic frequencies, electron affinities, ionization energies, and density of states distributions show the contracted set to be a viable replacement for the full basis set. This result is obtained using both the B3LYP and BPW91 exchange-correlation potentials in density functional theory.     

张青莲教授及其原子量新值测定研究

张青莲教授是中国科学院院士,我国同位素化学的奠基人.本文介绍他在90高龄之际在原子量新值测定方面所取得的杰出成就.从1990年代初以来,他主持一个科研小组采用质谱法,实施了测定10项原子量新值的长期计划.至2001年7月已经有In、Ir、Sb、Eu、Ce、Er、Ge、Dy和Zn等9个原子量新值被国际纯粹与应用化学联合会(IUPAC)的原子量与同位素丰度委员会(CAWIA)正式确定为原子量的国际新标准;另外一个Sm原子量新值也于2005年被国际组织确认.     

A finite expansion method for the calculation and interpretation of molecular electrostatic potentials

Because it is useful to have the molecular electrostatic potential as an element in a complex scheme to assess the toxicity of large molecules, efficient and reliable methods are needed for the calculation and characterization of these potentials. A multicenter multipole expansion of the molecular electron charge density calculated with a limited Gaussian basis set is shown here to have only a finite number of nonzero terms from which the molecular electrostatic potential can be calculated. The discrete contributions to the electrostatic potentials from the terms of this expansion provide a physically meaningful decomposition of the potential and a means for its characterization. With pyrrole as an example, the electrostatic potential calculated from this finite expansion of the electron density is compared to that obtained from exact calculations from the same wave function. Good agreement is obtained at distances greater than 1.5 A from any atom in the molecule. In contrast, rearrangement of the terms into an expansion corresponding only to Mulliken atomic charges and dipoles yields a decomposition that produces electrostatic potentials which agree less well with the exact potential. This discrepancy is attributable to the neglect of terms due to higher moments.     

Optimized Atomic Partial Charges and Radii Defined by Radical Voronoi Tessellation of Bulk Phase Simulations

We present a novel method for the computation of well-defined optimized atomic partial charges and radii from the total electron density. Our method is based on a two-step radical Voronoi tessellation of the (possibly periodic) system and subsequent integration of the total electron density within each Voronoi cell. First, the total electron density is partitioned into the contributions of each molecule, and subsequently the electron density within each molecule is assigned to the individual atoms using a second set of atomic radii for the radical Voronoi tessellation. The radii are optimized on-the-fly to minimize the fluctuation (variance) of molecular and atomic charges. Therefore, our method is completely free of empirical parameters. As a by-product, two sets of optimized atomic radii are produced in each run, which take into account many specific properties of the system investigated. The application of an on-the-fly interpolation scheme reduces discretization noise in the Voronoi integration. The approach is particularly well suited for the calculation of partial charges in periodic bulk phase systems. We apply the method to five exemplary liquid phase simulations and show how the optimized charges can help to understand the interactions in the systems. Well-known effects such as reduced ion charges below unity in ionic liquid systems are correctly predicted without any tuning, empiricism, or rescaling. We show that the basis set dependence of our method is very small. Only the total electron density is evaluated, and thus, the approach can be combined with any electronic structure method that provides volumetric total electron densities—it is not limited to Hartree–Fock or density functional theory (DFT). We have implemented the method into our open-source software tool TRAVIS.     

Transformation of Bloch representation into atomic orbital representation and combined matrix element calculation technique for spatially bounded basis functions in crystals

A method is proposed for transforming the Hamiltonian from Bloch to atomic function representation. For spatially bounded functions, this is a rigorous method based on solution of a certain algebraic system of equations. Unlike the conventional procedure based on integration over the Brillouin zone, the new method requires knowledge of the matrix elements of the Bloch representation only at several points of the Brillouin zone. The number of these points is determined by the trimming radius for the spatially bounded functions and by the lattice constant. The method can be used for calculating matrix elements in a basis of atomic functions and for reducing computations in matrix element calculations of the Bloch representation for procedures using numerical integration.     

Deconvolution of STM images using entropy as a regularization functional

The Maximum Entropy approach is applied to restore and sharpen scanning tunneling microscopy (STM) images with atomic resolution. Based on the STM theory of Tersoff and Hamann the process of data acquisition can be approximated by the convolution of a localised atomic density of states (i.e. narrow spots in the reconstruction) of the sample and a Gaussian resolution function which limits the resolution. In STM practice a good and robust estimation of the atomic core positions is necessary for different reasons, such as to be able to calculate the characteristics of the atomic lattice or to study non-periodicities.     

Deconvolution of STM images using entropy as a regularization functional

The Maximum Entropy approach is applied to restore and sharpen scanning tunneling microscopy (STM) images with atomic resolution. Based on the STM theory of Tersoff and Hamann the process of data acquisition can be approximated by the convolution of a localised atomic density of states (i.e. narrow spots in the reconstruction) of the sample and a Gaussian resolution function which limits the resolution. In STM practice a good and robust estimation of the atomic core positions is necessary for different reasons, such as to be able to calculate the characteristics of the atomic lattice or to study non-periodicities.     

Molecule‐specific determination of atomic polarizabilities with the polarizable atomic multipole model

Recently, many polarizable force fields have been devised to describe induction effects between molecules. In popular polarizable models based on induced dipole moments, atomic polarizabilities are the essential parameters and should be derived carefully. Here, we present a parameterization scheme for atomic polarizabilities using a minimization target function containing both molecular and atomic information. The main idea is to adopt reference data only from quantum chemical calculations, to perform atomic polarizability parameterizations even when relevant experimental data are scarce as in the case of electronically excited molecules. Specifically, our scheme assigns the atomic polarizabilities of any given molecule in such a way that its molecular polarizability tensor is well reproduced. We show that our scheme successfully works for various molecules in mimicking dipole responses not only in ground states but also in valence excited states. The electrostatic potential around a molecule with an externally perturbing nearby charge also exhibits a near‐quantitative agreement with the reference data from quantum chemical calculations. The limitation of the model with isotropic atoms is also discussed to examine the scope of its applicability. © 2012 Wiley Periodicals, Inc.     

Improvements in thermospray flame furnace atomic absorption spectrometry

In thermospray flame furnace atomic absorption spectrometry (TS-FF-AAS) a nickel atomization tube is placed in the acetylene/air flame on a holder built onto a standard AAS burner head. The liquid to be analyzed is transported by a low or high-pressure pump through a very hot, simple, inexpensive ceramic capillary tip acting as a flame-heated thermospray into the flame furnace. This results in complete sample introduction and increases the residence time of the sample in the absorption volume. This leads for 17 elements to a 3-110-fold improvement in the power of detection compared to conventional flame AAS. The absolute detection limits (3s values, N=25) lie between 0.2 μg l⁻¹ (Zn) and 310 μg l⁻¹ (Se) according to the element. The R.S.D. (N=15) is 1.4-5.5% according to the element and applied concentration. TS-FF-AAS can easily be incorporated on any standard flame AAS instrument and can be automated with a standard autosampler.     

Multimolecular polyhedra and QSPR

A multimolecular polyhedron (MP) is defined when studying molecular sets. When any molecular set is described using some chosen \(N\) -dimensional vector tags attached to every molecular object in the set, thus forming a tagged set, then the tag set also forms a MP. In the particular case when the molecular tags are density functions, then he quantum object set formed in this manner also defines some MP in \(\infty \) -dimensional space. In principle, MP are defined with respect an arbitrary origin, but once constructed one can shift it in two natural ways: (a) by each vertex at a time and (b) once for all by means of the polyhedron centroid. The quantum QSAR frames, which can be constructed following these two origin shift procedures, provide two not so different results when used for property evaluation. The differences between both shifting techniques are here revealed and discussed. A single density function for a given molecule is also studied from this point of view as a sequel of the previous study of MP.     

Unbiased auxiliary basis sets for accurate two-electron integral approximations

We propose Cholesky decomposition (CD) of the atomic two-electron integral matrix as a robust and general technique for generating auxiliary basis sets for the density fitting approximation. The atomic CD (aCD) auxiliary basis set is calculated on the fly and is not biased toward a particular quantum chemical method. Moreover, the accuracy of the aCD basis set can be controlled with a single parameter.     

Quality specifications for evaluation and comparison of performance among external quality assessment schemes in occupational and environmental laboratory medicine

Quality specifications (QS) are proposed for lead in blood and for aluminium, copper, selenium and zinc in serum as part of the aim to set standards of performance for laboratories so that results can be demonstrated to be fit for the purpose to which they are applied. The QS were established taking account of the analytical state-of-the-art, physiological variations in the concentrations of the analyte and the clinical purpose for which the assay is to be used. A procedure was devised that uses these QS to give equivalence of assessment among external quality assessment schemes (EQAS), thus avoiding conflicting information which has been demonstrated in the past. Advantages of this procedure are: to provide direct comparison of performance of laboratories taking part in different schemes, to provide equivalence of assessment of laboratory performance necessary to establish mutual recognition agreements, and to demonstrate the fitness for purpose of results from participants.Presented at the Eurachem PT Workshop September 2005, Portorož, Slovenia