Application of the many-body perturbation theory by using localized orbitals

Diagrammatic formulation of the many-body perturbation theory is investigated when both the occupied orbitals and the virtual ones are localized, i.e., they are unitary transforms of the canonical Hartree–Fock orbitals. All diagrams representing ground state correlation energy can be generated through fifth order. For cyclic polyenes C₆H₆ and C₁₀H₁₀ as model systems, the energy corrections are calculated in the Pariser–Parr–Pople approximation for a wide range of the coupling constant β^?1, through fourth order including some fifth order terms. The results are compared to those obtained by other methods: perturbation theory by using canonical orbitals and full CI. The effect of neglecting contributions from orbitals localized into neighboring sites is also studied.     

Cation influence on the structure and electron density of water in some Men+·H2O complexes

The cation influence on the water molecule in the Li⁺·H₂O, Be²⁺·H₂O, Mg²⁺·H₂O and A1³⁺·H₂O complexes has been studied by means of quantum-mechanical ab initio calculations. A number of general trends are noted. (1) The calculated equilibrium water O-H distances increase with increasing binding energies, i.e. in the order Li⁺, Mg²⁺, Be²⁺, Al³⁺. The H-O-H angles differ by about ±1 ° from the calculated equilibrium angle for the free H₂O molecule; the variation has no systematic trend. (2) The electron density redistribution accompanying the change in the internal H₂O geometry in these complexes is considerably smaller than the redistribution brought about by the direct influence of the external field. (3) The harmonic O-H stretching force constant decreases with increased cation-water bonding. (4) The qualitative features of the density changes are very similar for the four complexes. The magnitudes of the interactions follow the relation Li⁺ < Mg²⁺ < Be²⁺ Al³⁺. An increased polarization of the H₂O molecule occurs with electron migration from the H atoms towards the O atom and an accumulation of electron charge approximately at the centre of the Meⁿ⁺—O bond, especially in Be²⁺·H₂O and A1³⁺·H₂O. An electron deficiency is found in the lone-pair region.     

Studies of chemical hardness and Fukui function using the exact solution of the density functional theory

Neal's procedure has been applied to determine the electron density ρ(x) for the H₂ molecule. The chemical hardness has been calculated employing the ab initio and density functional theory methods and the values are found to be reasonably good. The principle of maximum hardness (PMH) was tested. Fukui functions and the distribution of electron density around the internuclear distance were studied employing the electron density of the H₂ molecule. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 4–10, 2001     

Nonempirical Description of the Atmospherically Important Anionic Species. III. Hydrated Nitrogen Dioxide Anions

Neutral and negatively charged NO₂(H₂O) _n clusters are simulated at the second order of the Møller–Plesset perturbation theory with 6-31G basis set extended with diffuse and polarization functions on all nuclei. For better reliability, configuration interaction and multiconfiguration self-consistent field calculations with the active spaces, formed by all single and double excitations to the basic determinant, are carried out. The weak binding of a neutral NO₂ molecule to water clusters is provided by its coordination to two water molecules, either directly H bonded to each other or joined in an H-bond network via the third molecule. The presence of an excess electron strongly decreases the summary energy of the NO₂(H₂O) _n system, so that its adiabatic affinity exceeds the summary affinity of NO₂ and water system, although the excess electron is localized predominantly by NO₂ fragment.     

Ab initio study,including electron correlation,of the electronic structures,the dipole moments,the static polarizabilities and of the harmonic force fields of H2CO,H2CS and H2SiO

Ab initio calculations including electron correlation (on the PNO-CI and CEPA-PNO levels) are carried out for the isovalence electronic molecules H₂CO, H₂CS and H₂SiO, and for comparison also for H₂O and CO. The CEPA equilibrium distances are accurate to within 0.003 Å, while SCF results show significantly larger errors. The harmonic force constants on CEPA level are satisfactory as well, but for stretching of double or triple bonds inclusion of singly substituted configurations is imperative. Dipole moments were obtained with an error of 0.1 Debye from CEPA calculations with sufficiently large basis sets and inclusion of singly substituted configurations. The dipole polarizabilities are less sensitive to correlation effects but require larger basis sets.The population analysis reveals that the SiO bond in H₂SiO is highly polar and thatd-AO's cannot be regarded as valence AO's in any of the molecules of this study. The binding energy of H₂SiO (with respect to H₂Si(¹ A ₁) + O(³ P)) is predicted as 140 ± 5 kcal/mol. The contributions of different pairs in terms of localized orbitals to the correlation energy of the molecules of this study are analyzed.     

Localized molecular orbital studies in momentum space. I. compton profiles of 1s core electrons and hydrocarbons

The calculations of momentum space properties for the polyatomic molecules CH₄, C₂H₄ and C₂H₆ using localized molecular orbitals of double zeta quality basis sets are presented. The LMO analysis shows that localized and canonical core electrons have different momentum space properties, and that in agreement with the experimental data of Eisenberger and Marra one can distinguish the momentum properties of the CC single and double bonds. The effect of environment on a bond is seen by comparing the CH bond in these three molecules.The concept of electron pair size is introduced as a quantitative guide for interpreting momentun space properties.     

Polarized neutron diffraction and its application to spin density studies

Spin density distributions in molecular compounds containing unpaired electrons have been studied by polarized neutron diffraction (PND). The spin density distributions provide a unique perspective of the magnetic properties of the compounds. The background and fundamentals of polarized neutron diffraction are summarized in this review, followed by examples of applications in inorganic and organic chemistry. Spin densities in several compounds that are obtained by polarized neutron diffraction are highlighted. Spin densities in single molecular magnet [Fe₈O₂(OH)₁₂(tacn)₆]⁸⁺ and cyano-bridged K₂[Mn(H₂O)₂]₃[Mo(CN)₇]₂·6H₂O demonstrate how to obtain magnetic interaction in the complexes by PND. PND studies of Ru(acac)₃, containing one single unpaired electron, show small spin densities in this complex. Finally the use of PND in studying nitronyl nitroxide radicals is given. Our goal in this review is to illustrate how PND functions and how it serves as a sensitive tool in directly probing spin density in molecules.     

A pseudopotential study of the hydrogen bond in H2O·H2S,H2S·H2S and H2O·H2Se systems

Intermolecular potential energy curves for the hydrogen bonded systems H₂O·H₂S, H₂O·H₂Se and H₂S·H₂S were calculated with nonempirical pseudopotentials using optimized-in-molecules basis sets augmented by polarization functions. The H₂O·H₂O interaction energy curve has been also considered as a test case. The present results for H₂O·H₂S and H₂S·H₂S indicate much weaker intermolecular interactions than those found in previous ab initio calculations. The H₂O·H₂Se interaction was found to be quite similar to H₂O·H₂S.This work was partly supported by the Polish Academy of Sciences within the Project PAN-09, 7.1.1.1On leave from Quantum Chemistry Laboratory, Dept. of Chemistry, University of Warsaw, Pasteura 1, 02-093. Warsaw, Poland     

CEPA calculations of potential energy surfaces for open-shell systems.: IV. Photodissociation of H2O in the A1B1 state

A three-dimensional potential energy surface for the photodissociation of H₂O in its lowest excited singlet state $\text{A}$¹B₁ in C_2v or $\text{A}$¹A″ in C₃ symmetry, respectively, has been calculated with quantum-chemical ab initio methods including electron correlation. The main features of the surface are discussed and qualitative explanations are given for the experimentally observed vibrational and rotational excitations of the product OH(²Π) radicals. The surface will be used in subsequent investigations of the dynamics of the H₂O photodissociation process.     

Nuclear magnetic isoscreening lines for O-O and O-H bonds: The second-order magnetic parameters of the H2O2 molecule

A variational method has been used with a basis of Gaussian atomic orbitals and an additive scheme based on localized molecular fragments to calculate the molar magnetic susceptibility and nuclear magnetic isoscreening line diagrams for O-O and O-H bonds, as well as and (for the protons) in the H₂O₂ molecule for the cis, trans, and twisted configurations. The molecular wave functions have been calculated by the INDO method and localized ones by the Edmiston-Rudenberg method, together with ab initio ₀ localized by Boys' method. It is found that and are substantially dependent on the bond lengths.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 4, pp. 482–487, July–August, 1986.     

Theoretical study of isomerism of compounds of N2 and N2H2 molecules with aluminum clusters Al13 and Al12Ti

Segments of the potential energy surfaces corresponding to successive elementary stages of multistep fragmentation of nitrogen and diimine molecules upon their reaction with the aluminum cluster Al₁₃ and its doped analogue Al₁₂Ti have been calculated by the density functional theory method. The minimum energy pathways of these reactions have been calculated for the stages of physisorption, chemisorption, and N₂ and N₂H₂ fragmentation with different ways of insertion of fragments into the Al₁₃ and Al₁₂Ti cages. Relative energies, structural characteristics, and vibrational frequencies of coordinated and fragment isomers have been calculated, the barriers separating these isomers have been evaluated, and molecular diagrams of the reactions have been constructed. The effect of doping on the relative energies of intermediates and activation barriers has been considered. A conclusion has been drawn that doping with titanium should facilitate the reactions of molecular nitrogen with aluminum clusters. Unusual isomers with a five- and six-coordinate nitrogen atom N* have been localized. The results are compared with the data of analogous previous calculations of the PES of isomers corresponding to stepwise fragmentation of an acetylene molecule in related Al₁₃C₂H₂ and Al₁₂TiC₂H₂ derivatives.     

Dynamic electron transfers in B2H6 and Cu(PH3)2(BH4)

In order to investigate the coupling of molecular vibrations and electron distribution, dynamic electron transfers in B₂H₆ and Cu(PH₃)₂(BH₄) are lated by using a new variational method. In both molecules, the dynamic electron density near bridging hydrogen atoms decreases to form the density valley by exciting specific vibrational modes. On the other hand, in both sides of the valley density hills grow up. For these molecules, similar contour maps are given by the modes with different symmetry which have large contribution of the bridging ligands. While the dynamic electron transfer of B₂H₆ arises in symmetric form, the vibrational modes of the Cu complex gives the asymmetric redistribution of the dynamic electron density. This is attributed to the difference of the symmetry between the two molecules.     

Aromaticity in Group 14 homologues of the cyclopropenylium cation

The nature of the bonding and the aromaticity of the heavy Group 14 homologues of cyclopropenylium cations E₃H₃⁺ and E₂H₂E′H⁺ (E, E′=C–Pb) have been investigated systematically at the BP86/TZ2P DFT level by using several methods. Aromatic stabilization energies (ASE) were evaluated from the values obtained from energy decomposition analysis (EDA) of charged acyclic reference molecules. The EDA‐ASE results compare well with the extra cyclic resonance energy (ECRE) values given by the block localized wavefunction (BLW) method. Although all compounds investigated are Hückel 4n+2 π electron species, their ASEs indicate that the inclusion of Group 14 elements heavier than carbon reduces the aromaticity; the parent C₃H₃⁺ ion and Si₂H₂CH⁺ are the most aromatic, and Pb₃H₃⁺ is the least so. The higher energies for the cyclopropenium analogues reported in 1995 employed an isodesmic scheme, and are reinterpreted by using the BLW method. The decrease in the strength of both the π cyclic conjugation and the aromaticity in the order C?Si>Ge>Sn>Pb agrees reasonably well with the trends given by the refined nucleus‐independent chemical shift NICS(0)_πzz index.     

Study of correlation holes. II. CI calculations on model polyatomic systems

The shape of correlation holes in many-electron systems is at present scarcely known, even where correlated wave functions are available. We investigate here the kind of electron correlation brought about by configuration interaction (CI ), within a given basis set, in the wavefunction of a polyatomic system. The model ring system H₆ (in two different bonding circumstances) and H₁₄ have been chosen for a detailed study, because of their paradigmatic importance. We set out the equal-spin and different-spin correlation holes as obtained from complete CI calculations in H6 and partial ct in H₁₄, both within a minimal basis set. We basically find the spinless correlation as being short range, while the spin-dependent correlation holes show long-range oscillations of antiferromagnetic character. We also present a natural spin-geminal analysis of the two-body reduced density matrices in these systems; we find a peculiarity possibly related to the long-range correlation discussed above. Finally, we compare the electron correlation as given from our CI wavefunction to other pictures of electron correlation, as obtained essentially from alternant molecular orbital wave functions and from the electron–gas literature.     

A theory of molecules in molecules IV. Application to the Hydrogen Bonding Interaction in NH3 · H2O

The theory of molecules in molecules introduced in previous articles is applied to study the hydrogen bonding interaction between an ammonia molecule as proton acceptor and a water molecule as proton donor. The localized orbitals which are assumed to be least affected by the formation of the hydrogen bond are transferred unaltered from calculations on the fragments NH₃ and H₂O, the remaining orbitals are recalculated. A projection operator is used to obtain orthogonality to the transferred orbitals. Additional approximations have been introduced in order to be able to save computational time. These approximations can be justified and are seen to lead to binding energies and bond lengths which are in satisfactory agreement with the SCF values. The point charge approximation for the calculation of the interaction energy between the two sets of transferred localized orbitals is, however, not applicable in this case. An energy analysis of the effect of the hydrogen bond on the localized orbitals of the two fragments is given.     

Measurement of electron density utilizing the Hα-line from laser produced plasma in air

The electron density in a laser produced plasma experiment was measured utilizing the Stark broadening of the H_α-line at 656.27 nm. This line results from the interaction of the Nd:YAG laser at the fundamental wavelength of 1.06 μm with a plane solid aluminum target in a humid air. The measurements were repeated at several delay times (0–10 μs) and at a fixed gate time of 1 μs. The electron density from the optically thin Al II-line at 281.62 nm was measured in parallel from the same spectra. The electron density was found in the range from 10¹⁸ cm^− 3 down to 6 × 10¹⁶ cm^− 3 at longer delay time. The electron density from the H_α-line using the Griem's standard theory was compared with the predictions of other model due to Gigosos et al. The agreement between the measured electron density from both the H_α-line and the Al II-line would confirm the reliability of utilizing the H_α-line as an electron density standard reference line in LIBS experiments. Several important features characterize the H_α-line: it is a well isolated line, it gives large signal to background ratio, it lasts a long time after the termination of the laser (up to 10 μs), its Stark width is relatively large and does not exhibit self-absorption.     

Metastable phase equilibria in the systems K2SO4 + K2B4O7 + H2O and KCl + K2B4O7 + H2O at 308.15 K

Experimental studies on the metastable solubilities and physicochemical properties (density and refractive index) in the ternary systems K₂SO₄ + K₂B₄O₇ + H₂O and KCl + K₂B₄O₇ + H₂O at 308.15 K were determined with the method of isothermal evaporation. According to the experimental results, the phase diagrams of the two ternary systems were plotted. In the phase diagrams, there are both two isotherm evaporation curves, one eutectic point corresponding to K₂SO₄ + K₂B₄O₇ · 4H₂O, and KCl + K₂B₄O₇ · 4H₂O, respectively. Both of the ternary systems belong to a simple eutectic type, and neither double salts nor solid solutions formed in the ternary systems. A comparison of the stable and metastable phase diagrams of the ternary systems K₂SO₄ + K₂B₄O₇ + H₂O and KCl + K₂B₄O₇ + H₂O shows that the supersaturated phenomenon of potassium borate tetrahydrate is significant and easier to appear the metastable behavior.     

Clathrate formation in (i-C5H11)4−k (C4H9) k NF−H2O (k=1,2,3) binary systems

Phase diagrams of some binary aqueous systems with tetraalkylammonium fluorides are examined. The size of the hydrophobic moiety of the guest is consecutively varied in the series (i-C₅H₁₁)_4−k(C₄H₉)_kNF (k=0, 1, 2, 3) by replacing bulky isoamyl radicals with n-butyl radicals. Changes in clathrate formation caused by variations of the sizes and forms of guests are analyzed in the series (i-C₅H₁₁)_k−4(C₄H₉)_kNF−H₂O (k=0, 1, 2, 3, 4). All tetraisoamylammonium fluoride hydrates are more stable than other hydrates of this series. The stability of the compounds increases due to the fact that the isoamyl radicals use the host cavities more effectively than the butyl radicals. In all hydrates of the series, tetragonal structures-I (TS-I), which were earlier thought typical only for hydrates of tetrabutylammonium salts, are formed. Hydrates of the orthorhombic system are formed until three isoamyl radicals have been replaced by butyl radicals. Hydrates with 26–28 water molecules (mp 27.4–34.6°C) are the most stable hydrates of the series, except for i-AmBu₃NF·25.9 H₂O, melting 0.3°C lower than the tetragonal hydrate in the same system. All compounds are defined chemically, and for some of them crystal data are given. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Institute of Physical Chemistry, Polish Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 3, pp. 501–508, May–June, 1995. Translated by L. Smolina     

On the use of the Hα spectral line to determine the electron density in a microwave (2.45 GHz) plasma torch at atmospheric pressure

The electron density of an argon microwave (2.45 GHz) plasma flame generated at atmospheric pressure has been determined by using the Stark broadening of the experimentally measured H_α line emitted by the discharge. The H_β line was not observable under the experimental conditions of this discharge. Two methods have been employed to obtain the electron density from the Stark broadening of the H_α line. The first used the Gigosos–Cardeñoso computational model that considers the strong broadening of the H_α line by ionic dynamics. Alternatively, a second method based on a calibration of Stark broadenings of H_α and H_β lines offered a simpler way to obtain the electron density.     

Challenges in the use of density functional theory to examine catalysis by M‐doped ceria surfaces

For CeO₂ or M‐doped CeO₂ catalysts, reliable energetics associated with surface reactivity requires accurate representation of oxidized and reduced metal states. Density functional theory (DFT) is used extensively for metals and metal oxides; however, for strongly correlated electron materials, conventional DFT fails to predict both qualitative and quantitative properties. This is the result of a localized electron self‐interaction error that is inherit to DFT. DFT+U has shown promise in correcting energetic errors due to the self‐interaction error, however, its transferability across processes relevant to surface catalysis remains unclear. Hybrid functionals, such as HSE06, can also be used to correct this self‐interaction error. These hybrid functionals are computationally intensive, and especially demanding for periodic surface slab models. This perspective details the challenges in representing the energetics of M‐doped ceria catalyzed processes and examines using DFT extensions to model the localized electronic properties. © 2013 Wiley Periodicals, Inc.