Population Analysis Methods Research Articles

The Curious Case of the Allyl Ligand: A Study in Applying the 18-Electron Rule

The 18-electron rule is an incredibly powerful tool for explaining the properties and reactivities of organometallic complexes. With the rule, however, comes the difficulty of choosing a method of implementing it, i.e. what many popular texts refer to as the “donor-pair” (ionic) method or the “neutral-ligand” method. The choice becomes particularly difficult when ligands can be counted in multiple ways via the donor-pair method, as in the case of the allyl ligand. In this investigation we hope to show that a choice of counting method can be chosen based on experimental intuition, as supported by a density functional theory (DFT) investigation. The natural electronic charge of metals, the η3-π-allyl (or simply the allyl) ligand, and the η3-cyclopropenyl ligand are discussed for a variety of organometallic complexes. A variety of DFT exchange-correlation functionals and basis sets, coupled with the Natural Population Analysis method of Landis and Weinhold, reveal the allyl ligand’s charge in a complex can be traced back to its experimental precursor. These results emphasize that the 18-electron rule is not merely a bookkeeping device and that the donor-pair method in the case of the allyl ligand holds more utility than the neutral-ligand method.

Preferential chlorination vertices in cobaltabisdicarbollide anions. Substitution rate correlation with site charges computed by the two atoms natural population analysis method (2a-NPA)

Preferential chlorination sites resulting from sequential substitution reactions in the representative metallacarborane [3,3′-Co(1,2-C2B9H11)2]− have been studied by combining experimental and computational methods. Similarly to aromatic substitution, the preferential chlorination sites in metallacarborane and carborane anions are of kinetic origin. There is no site preference in thermodynamic terms; however, there are sites on which the reaction takes place more rapidly. Preferential chlorination numbers have been proven experimentally by mixing the substrate with incremental ratios of N-chlorosuccinimide at 194 ± 6 °C and analyzing the resulting samples by negative MALDI-TOF-MS. Two parameters Δy and πy have been developed which are indicators of the ease of synthesis of species with y chlorine substituents, relative to the species with y + 1 substituents, and the persistence of the y species, relative to that with y + 1, in excess of chlorinating agent. These parameters have been used to account for the rates of the reaction. They explain the largely known stability of the hexachlorinated cobaltabisdicarbollide anion along with the mono, and dichlorinated species, but strongly support the stability of the octachlorinated cobaltabisdicarbollide anion, a species never previously reported. An excellent correlation for the relative reaction rates has been found with the 2a-NPA charges on the non-chlorinated starting material. The 2a-NPA value for a bond is defined as the sum of the NPA charges of the two bonded atoms (e.g. B–H or C–H). 2a-NPA charges match the order of attack on the bonds.

PREVALENCE OF HETEROGENEOUS GLYCOPEPTIDE INTERMEDIATE RESISTANCE IN METHICILLIN-RESISTANT <i>STAPHYLOCOCCUS AUREUS</i>

Multidrug resistant Methicillin-Resistant Staphylococcus Aureus (MRSA) is a major cause of nosocomial and community acquired infections and is on the rise. The aim of this investigation was to explore the prevalence of MRSA and heterogeneous Glycopeptide Intermediate Staphylococcus Aureus (hGISA) in various clinical samples, to investigate the various antibiotic resistant determinant genes among these strains collected from north and west Indian hospitals and to evaluate the response of various drugs to these strains. A total of 413 clinical specimens collected from different hospitals were processed for the screening of S. aureus and MRSA. All the MRSA strains were further screened for hGISA on Mueller-Hinton agar containing 8 µg mL-1 teicoplanin or 6 µg mL-1 vancomycin. hGISA confirmed by the E-test method with a dense inoculum and a simplified method of population analysis. Susceptibility study was conducted according to the Clinical and Laboratory Standards Institute (CLSI) methods. Among 211/413 S. aureus clinical isolates, 61.6% (130/211) of the isolates were confirmed to be MRSA which included maximum isolates from pus, blood, urine, wound swab and ear swab samples in decreasing order. hGISA strains were found in 8/130 (6.1%) isolates. Vancoplus, a novel antibiotic adjuvant entity was found to be susceptible in 96.1 to 97.8% MRSA strains and showed intermediate response in 2.2 to 3.8% of isolates. Linezolid appeared to be second most active antibiotic with 48.0 to 81.2% susceptibility, followed by teicoplanin (41.3 to 56.2% susceptibility). There was 8.7 to 9.6% resistance observed in Linezolid which was increased to 48% in teicoplanin, to >60% in daptomycin and >75% in vancomycin. Interestingly, none of the isolates were susceptible to ceftriaxone and cefoperazone plus sulbactam. From the above study it can be concluded that prevelance of MRSA has reached a significant level and Vancoplus is the most effective drug in MRSA as well as hGISA organisms in comparison to comparator drugs.

Ab initio study of Pd-decorated single-walled carbon nanotube with C-vacancy as CO sensor

In this paper, the adsorption of CO onto Pd-decorated (5,5) single-walled carbon nanotube (Pd/SWCNT) and Pd-doped (5,5) single-walled carbon nanotube (Pd/SWCNT-V) has been investigated using ab initio studies. The larger binding energies and charges transfer show that the adsorption of CO onto Pd/SWCNT is more stable than that of CO onto Pd/SWCNT-V. The Pd/SWCNT can be utilized as good sensors for CO molecules due to strong binding energy and large electron charge transfer between the Pd/SWCNT and this molecule. Furthermore, the topological properties of the electron density distributions for intramolecular interactions have been analyzed in terms of the Bader theory of atoms in molecules. Finally, the natural population analysis method has been used to evaluate the Pd–C and Pd/CO interactions.

Unpaired electrons at the second‐order reduced density matrix level: Covalent bonding, and coulomb and fermi correlations in closed shell systems

AbstractThe usual one‐electron populations in atomic orbitals of closed shell systems are split into unpaired and paired at the (spin‐dependent) second‐order reduced density matrix level. The unpaired electron in an orbital is defined as the “simultaneous occurrence of an electron and an electron hole of opposite spins in the same spatial orbital,” which for simplicity is called “electropon.” The electropon population in a given orbital reveals whether and to what degree the Coulomb correlations, and hence, the chemical bonding between this orbital and the remaining orbitals of the system are globally favorable or unfavorable. The interaction of two electropons in two target orbitals reveals the quality (favorable or unfavorable) and the strength of the covalent bonding between these orbitals; this establish a bridge between the notion of “unpaired electrons” and the traditional covalent structure of valence‐bond (VB) theory. Favorable/unfavorable bonding between two orbitals is characterized by the positive/negative (Coulomb) correlation of two electropons of opposite spins, or alternatively, by the negative/positive (Fermi) correlation of two parallel spin electropons. A spin‐free index is defined, and the relationship between the electropon viewpoint for chemical bonding and the well‐known two‐electron Coulomb and Fermi correlations is established. Benchmark calculations are achieved for ethylene, hexatriene, benzene, pyrrole, methylamine, and ammonia molecules on the basis of physically meaningful natural orbitals. The results, obtained in the framework of both orthogonal and nonorthogonal population analysis methods, provide the same conceptual pictures, which are in very good agreement with elementary chemical knowledge and VB theory. © 2013 Wiley Periodicals, Inc.

A model population analysis method for variable selection based on mutual information

In many fields of chemistry and biology research, the routinely produced analytical data are usually of very high dimension. Thus, variable selection is essential to improve the prediction performance of models and to provide a better understanding of the underlying process that generated the data. Indeed, many kinds of methods have been developed for this purpose, and the variable selection method based on mutual information is one of them, where the relevance between the input variables and the response is maximized and the redundancy of the selected variables is minimized. However, several methods based on mutual information adopt a greedy search path so that the selected variable subset is most likely to be local minimum. To overcome this problem, model population analysis is used to build the search path. Therefore, a novel variable selection method based on information theory combined with model population analysis is proposed in this investigation. Using three real world datasets, the proposed method was tested and further compared with other methods. The results showed that the proposed method achieved competitive performance.

Theoretical, Kinetic and Mechanistic Studies of the Reaction between Dialkyl Acetylenedicarboxylates, Triphenylphosphine and Pyrrole in Organic Solvents

The kinetics of the reaction between triphenylphosphine, dialkyl acetylenedicarboxylates and pyrrole in dry organic solvents at different temperatures have been studied spectrophotometrically. The observed overall second rate constant ( k2)for reaction decreases with decreasing solvent dielectric constant and media temperature; k2 follows the Arrhenius equation, and the overall reaction is first order in both the dialkyl acetylenedicarboxylate and triphenylphosphine concentrations. The proposed mechanism has been evaluated, and the activation parameters Δ G≠, Δ S≠ and Δ H≠ for the first, rate-determining step, as an elementary reaction have been determined on the basis of Eyring equation. In addition, the Z- and E-isomers have been optimized at HF and B3LYP levels with the 6-311++G** basis set; the more stable is the E-isomer, in agreement with experimental data. Furthermore, to better understand the intramolecular interactions, atoms in molecules (AIM) calculations and natural population analysis (NPA) methods have been carried out. The 1H, 13C, and 31P NMR data of these ylides are consistent with results obtained from theoretical calculations.

Hydrogen bond studies in substituted imino-acetaldehyde oxime

The intramolecular hydrogen bond, molecular structure and vibrational frequencies of imino-acetaldehyde oxime and its twelve derivatives have been investigated by means of density functional (DFT) method with 6-311++G∗∗ basis set. The nature of these interactions, known as resonance assisted hydrogen bonds, has been discussed. As a geometrical indicator of a local aromaticity, the geometry-based HOMA index has been applied. Additionally the linear correlation coefficients between substituent constants and selected parameters in R position have been calculated. The results show that the hydrogen bond strength is mainly governed by the resonance variations inside the chelate ring induced by the substituent groups. The topological properties of the electron density distributions for OH⋯N intramolecular bridges have been analyzed in terms of the Bader theory of atoms in molecules (AIMs). Furthermore, calculated 1H NMR chemical shifts (δH) correlate well with the hydrogen-bond distance as well as electron density at the bond and ring critical points in the molecular electron density topography. Finally, the natural population analysis method has been used to evaluate the hydrogen bonding interactions.

Binding of piano‐stool Ru(II) complexes to DNA; QM/MM study

Ru(II) "piano-stool" complexes belong to group of biologically active metallocomplexes with promising anticancer activity. In this study, we investigate the reaction mechanism of [(η(6)-benzene)Ru(II)(en)(H(2)O)](2+) (en = ethylenediamine) complex binding to DNA by hybrid QM/MM computational techniques. The reaction when the Ru(II) complex is coordinated on N7-guanine from major groove is explored. Two reaction pathways, direct binding to N7 position and two-step mechanism passing through O6 position, are considered. It was found that the reaction is exothermic and the direct binding process is preferred kinetically. In analogy to cisplatin, we also explored the possibility of intrastrand cross-link formation where the Ru(II) complex makes a bridge between two adjacent guanines. Two different pathways were found, leading to a final structure with released benzene ligand. This process is exothermic; however, one pathway is blocked by relatively high initial activation barrier. Geometries, energies, and electronic properties analyzed by atoms in molecules and natural population analysis methods are discussed.

Local and nonlocal contributions to molecular first-order hyperpolarizability: A Hirshfeld partitioning analysis

Based on first-principles calculations, a decomposition scheme is proposed to investigate the molecular site-specific first-order hyperpolarizability (β) responses by means of Hirshfeld population analysis and finite field method. For a molecule, its β is decomposed into local and nonlocal contributions of individual atoms or groups. The former describes the response within the atomic sphere, while the latter describes the contributions from interatomic charge transfer. This scheme is then applied to six prototypical donor-acceptor (D-A) or D-π-A molecules for which the local and nonlocal hyperpolarizabilities are evaluated based on their MP2 density. Both the local and nonlocal parts exhibit site-specific characteristics, but vary differently with molecular structures. The local part depends mainly on the atomic attributes such as electronegativity and charge state, as well as its location in the molecule, while the nonlocal part relates to the ability and distance of charge delocalization within the molecule, increasing rapidly with molecular size. The proposed decomposition scheme provides a way to distinguish atomic or group contributions to molecular hyperpolarizabilities, which is useful in the molecular design for organic nonlinear optical materials.

Population analysis solution to hardness enhancement in TiCxN1−x

We investigated the hardness enhancement in titanium carbonitrides (TiCxN1−x) by the population analysis method based on first-principles calculations. Populations for bonds TiC and TiN in TiCxN1−x (0.25<x<0.75) are all positive. The enhanced hardness for titanium carbonitrides is well explained by overlap population analysis. Intrinsic hardness of TiCxN1−x has been calculated based on the obtained overlap populations. The calculated results are in good agreement with the available experimental data.

Computational study for the ylide isomers from the reaction between triphenylphosphine and dialkyl acetylenedicarboxylates in the presence of 6-chloro-2-benzoxazolethiol

Stable crystalline phosphorus ylides were obtained in excellent yields from the 1:1:1 addition reactions between triphenylphosphine and dialkyl acetylenedicarboxylates, in the presence of NH-heterocyclic compound, such as 6-chloro-2-benzoxazolethiol. These stable ylides exist in solution as a mixture of the two geometrical isomers as a result of restricted rotation around the carbon–carbon partial double bond resulting from conjugation of the ylide moiety with the adjacent carbonyl group. In the recent work, NMR study and the stability of the Z- and E-isomers were undertaken for the two rotamers of phosphorus ylides involving 6-chloro-2-benzoxazolethiol by atoms in molecules (AIM) and natural population analysis (NPA) methods. The relative energy for the two Z and E isomers was calculated at both HF/6-31G (d,p) and B3LYP/6-311++G (d,p) in the presence of a solvent medium (ethyl acetate) and gas phases. The results were in good agreement with those that obtained by the 1H, 31P and 13C NMR experimental data.

Methods for Computing Accurate Atomic Spin Moments for Collinear and Noncollinear Magnetism in Periodic and Nonperiodic Materials.

The partitioning of electron spin density among atoms in a material gives atomic spin moments (ASMs), which are important for understanding magnetic properties. We compare ASMs computed using different population analysis methods and introduce a method for computing density derived electrostatic and chemical (DDEC) ASMs. Bader and DDEC ASMs can be computed for periodic and nonperiodic materials with either collinear or noncollinear magnetism, while natural population analysis (NPA) ASMs can be computed for nonperiodic materials with collinear magnetism. Our results show Bader, DDEC, and (where applicable) NPA methods give similar ASMs, but different net atomic charges. Because they are optimized to reproduce both the magnetic field and the chemical states of atoms in a material, DDEC ASMs are especially suitable for constructing interaction potentials for atomistic simulations. We describe the computation of accurate ASMs for (a) a variety of systems using collinear and noncollinear spin DFT, (b) highly correlated materials (e.g., magnetite) using DFT+U, and (c) various spin states of ozone using coupled cluster expansions. The computed ASMs are in good agreement with available experimental results for a variety of periodic and nonperiodic materials. Examples considered include the antiferromagnetic metal organic framework Cu3(BTC)2, several ozone spin states, mono- and binuclear transition metal complexes, ferri- and ferro-magnetic solids (e.g., Fe3O4, Fe3Si), and simple molecular systems. We briefly discuss the theory of exchange-correlation functionals for studying noncollinear magnetism. A method for finding the ground state of systems with highly noncollinear magnetism is introduced. We use these methods to study the spin-orbit coupling potential energy surface of the single molecule magnet Fe4C40H52N4O12, which has highly noncollinear magnetism, and find that it contains unusual features that give a new interpretation to experimental data.

Electron and Spin Density Topology of the H‐Cluster and Its Biomimetic Complexes

AbstractThe catalytically active cluster of [FeFe]‐hydrogenase (H‐cluster) is unique due to its chemical composition and electronic and geometric structures. Protein crystallography revealed the presence of biologically unique diatomic ligands coordinating to the Fe centers and three light atoms bridging the sulfur atoms of its [2Fe]‐subcluster. The identity of the light atoms remains uncertain, even at close to atomic resolution (1.39 Å), as well as due to the lack of understanding at the molecular level of the cluster's biosynthetic pathway. By using all of the proposed ligand compositions, we carried out a comprehensive electronic structure analysis by evaluating the topology of the electron density and, particularly, the atomic spin density distribution derived from various population analysis methods for the free dithiolate ligands, the biomimetic [2Fe] complexes, and the entire H‐cluster embedded in its approximately 3.5 Å protein environment. In the biomimetic model complexes we found substantial spin density delocalization at the bridgehead of the dithiolate ligands. We attributed the presence of spin density to the through‐space spin polarization interaction between the paramagnetic iron centers and the bridgehead group, as represented by the ring critical points for the [Fe–(S–R–S)–Fe] metallacycles. However, this spin polarization of the bridgehead group vanishes for some of the biomimetic models, as well as for the 208‐atom computational model of the H‐cluster, due to a network of weak interactions. When the bridgehead group becomes part of a conduit for transmitting the spin polarization towards the terminal ends of each interaction network, such as the distal water or H‐bonded residues, the spin density vanishes. The variations of the Fe atomic spin densities were compared and contrasted for the proximal and distal iron sites in the crystallographic and the rotated conformations, respectively.

Effect of alkali metal ions on the pyrrole and pyridine π-electron systems in pyrrole-2-carboxylate and pyridine-2-carboxylate molecules: FT-IR, FT-Raman, NMR and theoretical studies

The FT-IR, FT-Raman and 1H and 13C NMR spectra of pyrrole-2-carboxylic acid (PCA) and lithium, sodium, potassium, rubidium and caesium pyrrole-2-carboxylates were recorded, assigned and compared in the Li → Na → K → Rb → Cs salt series. The effect of alkali metal ions on the electronic system of ligands was discussed. The obtained results were compared with previously reported ones for pyridine-2-carboxylic acid and alkali metal pyridine-2-carboxylates. Calculations for pyrrole-2-carboxylic acid and Li, Na, K pyrrole-2-carboxylates in B3LYP/6-311++G ** level and Møller–Plesset method in MP2/6-311++G ** level were made. Bond lengths, angles and dipole moments as well as aromaticity indices (HOMA, EN, GEO, I 6) for the optimized structures of pyrrole-2-carboxylic acid (PCA) and lithium, sodium, potassium pyrrole-2-carboxylates were also calculated. The degree of perturbation of the aromatic system of ligand under the influence of metals in the Li → Cs series was investigated with the use of statistical methods (linear correlation), calculated aromaticity indices and Mulliken, NBO and ChelpG population analysis method. Additionally, the Bader theory (AIM) was applied to setting the characteristic of the bond critical points what confirmed the influence of alkali metals on the pyrrole ring.

Characterizing electronic structure motifs inβ-UH3

Density-functional theory was used to evaluate the electronic structure of $\ensuremath{\beta}{\text{-UH}}_{3}$ over a range of unit-cell volumes. Using population analysis methods (projection and topological) the magnetic and electronic structure were probed. It was found that the topological analysis led to the description of the $\ensuremath{\beta}{\text{-UH}}_{3}$ crystal as partially ionic, with delocalization of electrons running across the U-U bonds that form one-dimensional chains in the (100), (010), and (001) directions. Magnetic moments were divided into delocalized (itinerant) moments running along the chains of the crystal, and localized moments, for the U atoms sited at the bcc sites. The experimental observation regarding the identical magnetic properties for the two distinct sites was shown to result from a coincidence in the moments and electronic configurations of the uranium atoms obtained at the equilibrium volume whereas these properties diverged at higher and lower cell volumes. The electronic structure was interpreted in terms of three primary categories of orbital overlap: U-U of the dissimilar sites, U-U of the chain sites, and U-H effects, each having separate volume dependencies. Analysis of the magnetovolumetric properties of $\ensuremath{\alpha}{\text{-UH}}_{3}$, in which U-U bonding at the chain sites does not occur, shows features that support this analysis.

Model Core Potential and All-Electron Studies of Molecules Containing Rare Gas Atoms†

Molecules HRgF (Rg = Ar, Kr, Xe, Rn) were studied at levels of theory that included electron correlation, taking relativistic effects into account either by using the recently developed parametrization of the extended model core potentials and basis sets or by using the Douglas-Kroll method with all-electron basis sets. Charge distributions were calculated according to Mulliken, Lowdin, and natural bond orbital methods of population analysis and the results of these methods were compared, confirming that bonding in these molecules corresponds to interaction between the fluoride anion and the RgH(+) moiety. In contrast to previously reported results, the present calculations show that the radon compound, HRnF, is more stable than compounds of the lighter congeners. Trends in the first ionization energies, bond lengths, energies of formation and decomposition, and harmonic vibrational frequencies were discussed and found to be consistent with the periodic trends of the atomic properties of the rare gas atoms.

Basis set dependence of atomic spin populations

To assess the basis set dependence of different population analysis methods, a comparison of spin populations for five open-shell systems (CF2CCH,C3H7,CH2OH, α-4-dehydrotoluene, and a binuclear Cu complex) was carried out across 13 standard basis sets, including minimal basis and variations of the Pople and correlation consistent families of basis sets. Mulliken, Löwdin, Bader’s Atoms in Molecules (AIM), Natural Population Analysis (NPA), Hirshfeld, and Minimum Basis Set Mulliken (MBS) are used. In contrast to the well known basis set sensitivity of the Mulliken population, we show that although the spin populations can be somewhat different, the MBS and the NPA methods trend the least with basis set choice.

Binding of ansa- and non-ansa-titanocene anticancer drugs to DNA: a DFT study

The complexes [Ti(η5-C2H4{CMe2CH2CH2CH=CH2})2Cl2] (1) and [Ti{Me2Si(η5-C5Me4)(η5-C5H3{CMe2CH2CH2CH=CH2})}Cl2] (2) exhibited significant antitumor activity, but the detailed mechanism of antitumor effect remains unknown. In current research, we studied the hydrated 1 and 2 bindings to potential biological targets, purine bases, and phosphate group, using density functional theory and IEF-PCM solvation models. Our calculations reveal that the monoaquated complex binding to guanine shows the lowest activation free-energy with 15.3 and 21.5 kcal/mol for the complexes 1 and 2, respectively. In the diaquaed 1, the lowest activation-free energy is 16.7 kcal/mol for the guanine and closely followed by the phosphate group is 18.3 kcal/mol, while the lowest activation-free energy is 16.9 kcal/mol for the complex 2 binding to the phosphate group. In addition, natural orbital population analysis (NPA) method was performed for the investigation of major electronic characteristics.

The Effects of Landscape Modifications on the Long-Term Persistence of Animal Populations

BackgroundThe effects of landscape modifications on the long-term persistence of wild animal populations is of crucial importance to wildlife managers and conservation biologists, but obtaining experimental evidence using real landscapes is usually impossible. To circumvent this problem we used individual-based models (IBMs) of interacting animals in experimental modifications of a real Danish landscape. The models incorporate as much as possible of the behaviour and ecology of four species with contrasting life-history characteristics: skylark (Alauda arvensis), vole (Microtus agrestis), a ground beetle (Bembidion lampros) and a linyphiid spider (Erigone atra). This allows us to quantify the population implications of experimental modifications of landscape configuration and composition.Methodology/Principal FindingsStarting with a real agricultural landscape, we progressively reduced landscape complexity by (i) homogenizing habitat patch shapes, (ii) randomizing the locations of the patches, and (iii) randomizing the size of the patches. The first two steps increased landscape fragmentation. We assessed the effects of these manipulations on the long-term persistence of animal populations by measuring equilibrium population sizes and time to recovery after disturbance. Patch rearrangement and the presence of corridors had a large effect on the population dynamics of species whose local success depends on the surrounding terrain. Landscape modifications that reduced population sizes increased recovery times in the short-dispersing species, making small populations vulnerable to increasing disturbance. The species that were most strongly affected by large disturbances fluctuated little in population sizes in years when no perturbations took place.SignificanceTraditional approaches to the management and conservation of populations use either classical methods of population analysis, which fail to adequately account for the spatial configurations of landscapes, or landscape ecology, which accounts for landscape structure but has difficulty predicting the dynamics of populations living in them. Here we show how realistic and replicable individual-based models can bridge the gap between non-spatial population theory and non-dynamic landscape ecology. A major strength of the approach is its ability to identify population vulnerabilities not detected by standard population viability analyses.