The self-interaction correction to the local spin density model: Effect on atomic momentum space properties

Perdew and Zunger showed that the exact energy density functional for the ground state is strictly self-interaction-free. However, the local spin density (LSD) approximation lacks this self-interaction correction (SIC). Perdew and Zunger studied the effect on coordinate-space properties of incorporating the SIC. In the present study we examine the effect of SIC on momentum space properties, viz. the electron momentum distribution, ⊂p″⊃ values, electron momentum densities and the Compton profiles for atoms He to Ar. A remarkable improvement is seen in all the momentum space properties of the SIC LSD model over the LSD model when compared to their near Hartree-Fock counterparts.     

Electron correlation in the GK state of the hydrogen molecule

The second excited (1)Sigma(g)(+) state of the hydrogen molecule, the so-called GK state, has a potential energy curve with double minima. At the united atom limit it converges to the 1s3d configuration of He. At large internuclear distances R, it dissociates to two separated atoms, one in the ground state and another in the 2p excited state. Radial pair density calculations and natural orbital analyses reveal unusual effect of electron correlation around the K minimum of the potential energy curve. As R>2.0 a.u., a natural orbital of sigma(u) symmetry joins the two natural orbitals of sigma(g) symmetry at smaller R. The average interelectronic distance decreases as the internuclear distance increases from R=2.0 to 3.0 a.u. Around R=3.0 a.u. the singly peaked pair density curve splits into two peaks. The inner peak can be attributed to the formation of the ionic electron configuration (1s)(2), where both 1s electrons are on the same nucleus. As the two 1s electrons run into different nuclei, one of the two 1s electrons is promoted to the 2p state, which results in the outer peak in the pair density curve. The Rydberg 1s2p configuration persists as the nuclei stretch, and becomes dominant at large R where four natural orbitals, two of sigma(g) and two of sigma(u) symmetry, become responsible.     

Partitioning schemes for the 2-matrix and the pair density

Several schemes are discussed for partitioning the second-order reduced density matrix Γ into two parts, Γ⁰ and Γ′. The Γ⁰s are based on the independent particle model and the Γ′s are corrections due to electron correlation. The difficulties of choosing a Γ⁰ that will serve as a suitable reference point for studying electron correlation are discussed. In order to compare alternative partitioning schemes, an atomic wave function for the ¹S ground state of the Be atom in the configuration-interaction approximation was selected. A fifty-two configuration wave function was computed and contour graphs were made of the total pair density Γ(1 2) and of the “correlation pair density” Γ′(1 2) for several choices of the reference Γ⁰.     

Oligomerization of N‐Heterocyclic Silylene into Zwitterionic Silenes

N‐Heterocyclic carbenes (NHC's) are known to serve as efficient substrates for the stabilization of various transient species possessing low‐valent Group 14 elements and for the generation of double E=C bonds. Herein, we report that the thermal tri‐ and tetramerizations of pyridoannulated silylene 1 lead to the formation of remarkably stable silenes 2 and 3 featuring zwitterionic distribution of electron density. Co‐oligomerization of 1 and its germanium analogue gives a related tetrameric product 4 containing low‐valent germanium atom stabilized by binding with the partial carbene‐character C atom. Bonding situations in 2 – 4 are best described as silene or germene with the significant zwitterionic distribution of electron density. The singlet diradical electronic state of 2 is 10 kcal mol^?1 higher than the ground state configuration.     

Ab initio theory for treating local electron excitations in molecules and its performance for computing optical properties

In this article, as a first step to develop an efficient approximation for predicting the molecular electronic excited state properties at ab initio level, we propose local excitation approximation (LEA). In the LEA scheme, the only local electron excitations within selected substructure (Chromophore) are treated to calculate the targeted excited state wavefunctions, whereas the other electron excitations (local electron excitations in other substructure and charge‐transfer excitations between different regions) are simply discarded. This concept is realized by using the localized molecular orbitals (LMO) localizing on the chromophore substructure. If the targeted transitions show the strong local character and the adequate substructure is selected as chromophore region, the LEA scheme can provide excited state properties without large loss of accuracy. The fatal slowdown of convergence speed of Davidson's iterative diagonalization due to the use of LMO can be avoided by additional transformation of LMOs. To assess the accuracy and efficiency of the LEA scheme, we performed test calculations using various compounds at configuration interaction single (CIS) and time‐dependent Hartree‐Fock (TDHF) level of theory. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Electronic structure of [(CpCr)[(CO)3M]]mu-Cot (M = Cr, Fe): a theoretical study

The electronic structure of two cyclooctatetraene-bridged dinuclear first-row transition metal complexes of the type [(CpM)[(CO)3M']]mu-Cot (M = Cr; M' = Fe (1), Cr (2)) was investigated by complete active space self-consistent field (CASSCF) calculations. In this context the differences in the binding capabilities of the complex fragments CpM and (CO)3M are discussed on the basis of extended Huckel molecular orbital (MO) calculations. The geometries used for the CASSCF calculations for complex 1 were obtained from the crystal structure. For 2 a model structure was established by geometry optimization using density functional methods. The CASSCF results agree well with the experimental findings and provide insight into the binding situation of the two compounds. Complex 1 can be regarded as being composed of a chromocene-like subunit CpCr(eta5-C5H5) and the fragment (CO)3Fe(eta3-C3H3). A direct metal-metal bond is found, involving one initially singly occupied orbital of each fragment, leading to a doublet ground state for 1 with the remaining unpaired electron localized at the chromium center. For 2 no such direct metal-metal bond can be recognized. A very weak direct metal-metal interaction is induced by electron donation from the Cot2- ligand into a formally unoccupied metal-metal binding orbital combination. In the quartet ground state all three unpaired electrons are localized at the chromium center of the formally doubly positive charged CpCr unit, on which complex fragment [(CO)3Cr(eta5-Cot)]2- acts like a cyclopentadienyl ligand. The coordination sphere of the chromium center of the CpCr unit resembles that of a metallocene metal center and its metal 3d occupation scheme corresponds to that of vanadocene.     

Excited states of nitro-polypyridine metal complexes and their ultrafast decay. Time-resolved IR Absorption, spectroelectrochemistry, and TD-DFT calculations of fac-[Re(Cl)(CO)3(5-nitro-1,10-phenanthroline)

The lowest absorption band of fac-[Re(Cl)(CO)3(5-NO2-phen)] encompasses two close-lying MLCT transitions. The lower one is directed to LUMO, which is heavily localized on the NO2 group. The UV-vis absorption spectrum is well accounted for by TD-DFT (G03/PBEPBE1/CPCM), provided that the solvent, MeCN, is included in the calculations. Near-UV excitation of fac-[Re(Cl)(CO)3(5-NO2-phen)] populates a triplet metal to ligand charge-transfer excited state, 3MLCT, that was characterized by picosecond time-resolved IR spectroscopy. Large positive shifts of the nu(CO) bands upon excitation (+70 cm(-1) for the A'1 band) signify a very large charge separation between the Re(Cl)(CO)3 unit and the 5-NO2-phen ligand. Details of the excited-state character are revealed by TD-DFT calculated changes of electron density distribution. Experimental excited-state nu(CO) wavenumbers agree well with those calculated by DFT. The 3MLCT state decays with a ca. 10 ps lifetime (in MeCN) into another transient species, that was identified by TRIR and TD-DFT calculations as an intraligand 3npi excited state, whereby the electron density is excited from the NO2 oxygen lone pairs to the pi system of 5-NO2-phen. This state is short-lived, decaying to the ground state with a approximately 30 ps lifetime. The presence of an npi state seems to be the main factor responsible for the lack of emission and the very short lifetimes of 3MLCT states seen in all d6-metal complexes of nitro-polypyridyl ligands. Localization of the excited electron density in the lowest 3MLCT states parallels localization of the extra electron in the reduced state that is characterized by a very small negative shift of the nu(CO) IR bands (-6 cm(-1) for A'1) but a large downward shift of the nu(s)(NO2) IR band. The Re-Cl bond is unusually stable toward reduction, whereas the Cl ligand is readily substituted upon oxidation.     

Use of the probability density function in the anharmonic theory of electron scattering by molecules

A scheme for the obtaining the electron density function W(Q ^s ) in a curvilinear vibrational coordinate system and scattering equation sM(s) is described in the framework of a vibrational model.Engels Anti-Aircraft Rocket Command Institute. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 6, pp. 33–37, November–December, 1989.     

An approximate quantitative analysis of non-equilibrium plasma transport for high density plasmas

For the evaluation of transport in high density plasmas numerical models have been developed in which simultaneously the conservation laws for mass, momentum and energy are solved. For high density plasmas, which are not too far from equilibrium the commonly used thermodynamic quantities are, electron temperature T_e, electron density n_e, heavy particle temperature and neutral density (or pressure). In this contribution an alternative formulation is described in which the plasma state is described by electron density ne and total pressure p and two non-equilibrium parameters: the deviation from Saha equilibrium of the neutral ground state (δb₁ = n₁/n₁ ^saha−1) and the deviation from thermal equilibrium between electrons and heavy particles δΘ = 1−T_h/T_e. The latter two parameters are zero in local thermodynamic equilibrium.

The advantage of this formulation is, that the transport coefficients and radiative properties can be reformulated as function of mainly n_e (at constant pressure), as the influences of non zero δb₁ and δΘ are small or can be explicitly given. As a result a simpler approximate formulation of the transport problem can be obtained. As an example the procedure is illustrated for atmospheric argon plasmas and for one aspect a comparison is made with work from e.g. E. Pfender.

     

Achieving Adaptive Aromaticity in Cyclo[10]carbon by Screening Cyclo[n]carbon (n=8−24)

Discovery of species with adaptive aromaticity (being aromatic in both the lowest singlet and triplet states) is particularly challenging as cyclic species are generally aromatic either in the ground state or in the excited state only, according to Hückel's and Baird's rules. Inspired by the recent realization of cyclo[18]carbon, here we demonstrate that cyclo[10]carbon possesses adaptive aromaticity by screening cyclo[n]carbon (n=8?24), which is supported by nucleus‐independent chemical shift (NICS), anisotropy of the current‐induced density (ACID), π contribution of electron localization function (ELF_π) and electron density of delocalized bonds (EDDB) analyses. Further study reveals that the lowest triplet state of cyclo[10]carbon is formed by in‐plane ππ* excitation. Thus, the major contribution to the aromaticity from out‐of‐plane π molecular orbitals does not change significantly in the lowest singlet state. Our findings highlight a crucial role of out‐of‐plane π orbitals in maintaining aromaticity for both the lowest singlet and triplet states as well as the aromaticity dependence on the number of the carbon in cyclo[n]carbon.     

Interesting properties of Thomas–Fermi kinetic and Parr electron–electron‐repulsion DFT energy functional generated compact one‐electron density approximation for ground‐state electronic energy of molecular systems

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a (nonlinear, approximate) density functional of three spatial dimension one‐electron density for an N‐electron system, which is tractable in the practice, is a long desired goal in electronic structure calculation. If the Thomas‐Fermi kinetic energy (～∫ρ^5/3d r ₁) and Parr electron–electron repulsion energy (～∫ρ^4/3d r ₁) main‐term functionals are accepted, and they should, the later described, compact one‐electron density approximation for calculating ground state electronic energy from the 2nd Hohenberg–Kohn theorem is also noticeable, because it is a certain consequence of the aforementioned two basic functionals. Its two parameters have been fitted to neutral and ionic atoms, which are transferable to molecules when one uses it for estimating ground‐state electronic energy. The convergence is proportional to the number of nuclei (M) needing low disc space usage and numerical integration. Its properties are discussed and compared with known ab initio methods, and for energy differences (here atomic ionization potentials) it is comparable or sometimes gives better result than those. It does not reach the chemical accuracy for total electronic energy, but beside its amusing simplicity, it is interesting in theoretical point of view, and can serve as generator function for more accurate one‐electron density models. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

3s Rydberg and cationic States of pyrazine studied by photoelectron spectroscopy

We have studied 3s(n-1 and pi-1) Rydberg states and D0(n-1) and D1(pi-1) cationic states of pyrazine [1,4-diazabenzene] by picosecond (2 + 1) resonance-enhanced multiphoton ionization (REMPI), (2 + 1) REMPI photoelectron imaging, He(I) ultraviolet photoelectron spectroscopy (UPS), and vacuum ultraviolet pulsed field ionization photoelectron spectroscopy (VUV-PFI-PE). The new He(I) photoelectron spectrum of pyrazine in a supersonic jet revealed a considerably finer vibrational structure than a previous photoelectron spectrum of pyrazine vapor. We performed Franck-Condon analysis on the observed photoelectron and REMPI spectra in combination with ab initio density functional theory and molecular orbital calculations to determine the equilibrium geometries in the D0 and 3s(n-1) states. The equilibrium geometries were found to differ slightly between the D0 and 3s states, indicating the influence of a Rydberg electron on the molecular structure. The locations of the D1-D0 and 3s(pi-1)-3s(n-1) conical intersections were estimated. From the line width in the D1 <-- S0 spectrum, we estimated the lifetime of D1 to be 12 fs for pyrazine and 15 fs for fully deuterated pyrazine. A similar lifetime was estimated for the 3s(pi-1) state of pyrazine by REMPI spectroscopy. The vibrational feature of D1 observed in the VUV-PFI-PE measurement differed dramatically from that in the UPS spectrum, which suggests that the high-n Rydberg (ZEKE) states converging to the D1 vibronic state are short-lived due to electronic autoionization to the D0 continuum.     

Quantum-chemical study of the structure and magnetic properties of mono- and binuclear Cu(II) complexes with 1,3-bis(3-(pyrimidin-2-yl)-1<Emphasis Type="Italic">H</Emphasis>-1,2,4-triazol-5-yl)propane

On the basis of X-ray crystallographic data on molecular copper complexes with 1,3-bis(3-(pyrimidin-2-yl)-1H-1,2,4-triazol-5-yl)propane, quantum-chemical optimization of their equilibrium structure has been performed by the density functional theory method with subsequent analysis of the electron density distribution by Bader’s atoms in molecules method and g-factor anisotropy calculation. The topological parameters of electron density at the Cu–N bond critical points have been considered, and the bond energies have been estimated using the Espinosa equation. A phenomenon of variable coordination of nitrate ions with Cu(II) ions in the inner coordination sphere of the mononuclear copper complex with 1,3-bis(3-(pyrimidin-2-yl)-1H-1,2,4-triazol-5-yl)propane has been revealed. The contributions of different components to the gfactor anisotropy have been analyzed in the framework of the gauge-independent atomic orbital method. The largest contribution to the g-factor is made by the orbital (Zeeman) and spin–orbit components accounting for very high averaged g-factor values of 2.1413 and 2.5636 for the doublet state of the mononuclear complex and the triplet state of the binuclear complex, respectively.     

Visualization of electron correlation in autoionizing states above the 3p threshold in magnesium

The conditional probability density has been calculated for a number of autoionizing states (AIS) in Mg above the 3p threshold. The correlation in such high energy AIS has not been extensively studied and provides insight into the rovibrator behavior of two-electron atoms. The calculations have been done by configuration interaction (CI) with a B-spline basis. This allows for the simultaneous study of the effects of electron correlation and the widths and angular distribution of photoelectrons in multiphoton ionization. The states have been assigned approximate vibrational quantum numbers, and a correlation between the approximate quantum numbers and the photoelectron distribution is observed. Probability distribution for one electron when the other, represented by the small spike, is at its most probable distance from the nucleus. This is a distribution for the doubly-excited 1S(e) state commonly labeled as the 4s2 state.     

On the electronic structure of molecular UO2 in the presence of Ar atoms: evidence for direct U-Ar bonding

Calculations via scalar-relativistic density functional theory (DFT) and ab initio CCSD(T) methodologies are used to explore the possibility of direct interactions between molecular UO2 and Ar atoms. The 3Hg electronic state of UO2, which is an excited state of the isolated molecule, exhibits significant bonding to Ar in the model complexes UO2(Ar) and UO2(Ar)5. The calculated vibrational frequencies of ground-state 3Phiu UO2 and UO2(Ar)5 with an (fphi)1(fdelta)1 electron configuration agree well with the observed frequencies of UO2 in solid neon and solid argon, respectively. The results strongly suggest that the ground electron configuration of UO2 changes from 5f17s1 to 5f2 when the matrix host is changed from neon to argon.     

An investigation of the two electron chemical bond calculating energy expectation values from density matrix partitionings. II. The heteronuclear case HeH+

Bond energy contributions calculated from first and second order density matrix terms as partitioned by Ruedenberg's procedure have been obtained for HeH⁺ in the ground state and in the first excited 1Σ⁺. For the chemically bonded ground state the full partitioning is investigated for all internuclear distances R. The wavefunctions used for calculating the density matrices are obtained from an SCF calculation at near Hartree-Fock quality, using Slater orbitals with exponents which for each R are optimized simultaneously with the coefficients. For the excited state a limited CI has been performed. The results for promotional, charge transfer, and interference terms for kinetic and potential bond contributions are presented in the form of energy plots E(R). Starting from the promoted atoms and subsequently allowing for charge transfer the importance of the electron interaction is demonstrated by the unusually low quasiclassical electron repulsion curve due to electronic charge transfer, which makes an essential contribution to the decrease in energy during bond formation.     

Strong exchange interactions between two radicals attached to nonaromatic spacers deduced from magnetic, EPR, NMR, and electron density measurements

A nitronyl-nitroxide (NIT) biradical D-NIT2 linked by a single double bond has been engineered and investigated in the solid state by a combination of X-ray diffraction, magnetic susceptibility measurement, EPR, as well as solid-state (1)H and (13)C NMR spectroscopies, and experimental electron density distribution. All techniques reveal that a double bond is a very efficient coupling unit for exchange interactions between two radical moieties. Using a Bleaney-Bowers model dimer (H = -JS(1)S(2)), a singlet-triplet energy gap of J = -460 K was found with the singlet state being the ground state. This very strong intramolecular interaction was confirmed by EPR measurements in CH(2)Cl(2) solution (6 10(-4) M) or dispersed in a polymer matrix at low concentration. In keeping with these unusual interactions, solid-state NMR signals of the biradical were found to be considerably less shifted than those found for related monoradicals. Temperature-dependent solid-state (13)C NMR spectra of D-NIT2 confirmed the very strong intramolecular coupling constant (J = -504 K). The electron density distribution of D-NIT2 was measured by high resolution X-ray diffraction, which also revealed that this biradical is an ideally conjugated system. The in-depth characterization includes the deformation maps and the observed electron density ellipticities, which exhibit a pronounced sigma-pi character of the O-N-C=C-N-O cores in keeping with an efficient electronic delocalization along the alkene spacer.     

Zero kinetic energy photoelectron spectroscopy of p-amino benzoic acid

We report studies of supersonically cooled p-amino benzoic acid using one-color resonantly enhanced multiphoton ionization and two-color zero kinetic energy (ZEKE) photoelectron spectroscopy. With the aid of ab initio and density functional calculations, vibrational modes of the first electronically excited state S(1) of the neutral species and those of the cation have been assigned, and the adiabatic ionization potential has been determined to be 64 540+/-5 cm(-1). A common pattern involving the activation of five vibrational modes of the cation is recognizable among all the ZEKE spectra. A propensity of Deltav=0, where v is the vibrational quantum number of the intermediate vibronic state from S(1), is confirmed, and the origin of this behavior is discussed in the context of electron back donation from the two substituents in the excited state and in the cationic state. A puzzling observation is the doublet splitting of 37 cm(-1) in the ZEKE spectrum obtained via the inversion mode of the S(1) state. This splitting cannot be explained from our density functional calculations.