Simultaneous presence of two charges or two spins in a linear polyene

Summary In this work we examine the ease of finding simultaneously two charges or two spins in various AO positions of a linear neutral polyene such as octatetraene. By applying the general multi-electron population analysis on a correlated wave function we calculate contributions from various ionic and covalent (in a probabilistic sense) resonance structures as well as electron-pair distributions with parallel and anti-parallel spins; the initial wave function used is a PPP + (quasi-total) CI wave function. Based on the second and fourth order anticommutation relations (and independently of the level of the MO wave function used) we show existing relationships between the quantities considered, as well as their constant behaviour. Covalent structures depend strongly on the parity and distance between the AO positions, while ionic ones arequasi-constant along the polyene. It is also shown that when the AO positions considered are non-vicinal, (+) and (–) charges appearmutually independent and the -electron conjugation has, rather surprisingly, no effect on them.     

Optimum hybrid orbitals in localized orbitals

Using the criterion for maximizing the projection of localized bond orbitals onto the space spanned by the occupied MO 's, a method for constructing hybrid orbitals of a molecule is described. For illustration purposes the method is applied to single-determinant closed shell wave functions, calculated by means of ab initio and semiempirical procedures, for the molecules of methane, acetylene, ethylene, ethane, propylene, butadiene, ammonia and hydrogen cyanide. The predictions of hybridization are briefly discussed.     

Natural polyelectron population analysis

A method to perform a polyelectron population analysis of correlated molecular orbital wave functions on the basis of natural atomic orbitals (NAO s), as given by Weinhold, is presented. The method allows calculations of the probabilities of finding various types of electronic events occuring in some target AO positions, including the contributions of ionic and covalent resonance structures. This method is general and neither the theory nor the developed algorithm limit the number of electrons and holes that can be considered. Thus, the analyzed MO wave function can be a usual CI or a MCSCF one, and apart from Weinhold's NAO s. any other type of orthogonal AO s can be used as analyzers, provided that these AO s are linear combinations of the SCF-AO s. Numerical applications are given for ethylene, formaldehyde, butadiene, and acroleine, by adopting various AO basis-set levels (STO ?4G , 4–31G , and 6–31G ) and by analyzing correlated wave functions (CISD ). Improvements in the polyelectron populations when increasing the quality of AO basis sets and the corresponding valence NAO s are revealed by several examples. Furthermore, it is shown that the electroegativity of oxygen in acroleine only has an effect on contributions of ionic and covalent resonance structures, but not on delocalization of the double bonds. 1993 John Wiley & Sons, Inc.     

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

The 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.     

Natural J-coupling analysis: interpretation of scalar J-couplings in terms of natural bond orbitals.

The natural J-coupling (NJC) method presented here analyzes the Fermi contact portion of J-coupling in the framework of finite perturbation theory applied to ab initio/density function theory (DFT) wave functions, to compute individual and pairwise orbital contributions to the net J-coupling. The approach is based on the concepts and formalisms of natural bond orbital (NBO) methods. Computed coupling contributions can be classified as Lewis (individual orbital contributions corresponding to the natural Lewis structure of the molecule), delocalization (resulting from pairwise donor-acceptor interactions), and residual repolarization (corresponding to correlation-like interactions). This approach is illustrated by an analysis of the angular and distance dependences of the contributions to vicinal (3)J(HH) couplings in ethane and to the long-range (6)J(HH) couplings in pentane. The results indicate that approximately 70% or more of the net J-coupling is propagated by steric exchange antisymmetry interactions between Lewis orbitals (predominantly sigma bonding orbitals). Hyperconjugative sigma to sigma delocalization interactions account for the remainder of the coupling. Calculated pairwise-steric and hyperconjugative-delocalization energies provide a means for relating coupling mechanisms to molecular energetics. In this way, J-coupling contributions can be related directly to the localized features of the molecular electronic structure in order to explain measured J-coupling patterns and to predict J-coupling trends that have yet to be measured.     

Molecular orbital studies of dinitrogen tetroxide and related molecules

Hartree-Fock LCAO MO calculations for N₂O₄ have been performed in a basis of symmetry orbitals formed from a minimal Slater basis set. Effects of rounding and truncation errors were minimized by the use of the symmetry basis, which also allowed the order or tilling of molecular orbitals to be specified independently of orbital energies. Convergence difficulties were overcome by combined use of the conjugate gradients method and Roothaan's iterative procedure; the method of steepest descents was less effective than either of these. Multicentre ‘non-NDDO’ two-electron integrals were evaluated by the gaussian expansion technique. The wavefunction obtained for the lowest state is NN antibonding, largely as a result of the filling of the 6b_1u antibonding sigma orbital in preference to the 6a_g bonding sigma orbital. There is only a small amount of NN pi-bonding. A bond energy analysis shows that the lowest state is markedly stabilized by NNO three-centre interactions.     

Real-space analysis of the exchange-correlation energy

The exchange-correlation energy of a many-electron system may be written as the electrostatic interaction between the electron density at position r and the density of the exchange-correlation hole at position r + u. If we average the hole over the entire system, we find that the energy is uniquely decomposed into contributions from various electronic separations u. We may also decompose the hole into contributions from parallel and antiparallel spins. We give several exact conditions which this system-averaged, spindecomposed exchange-correlation hole satisfies. Local spin density (LSD ) and generalized gradient approximations (GGAS ), are more appropriate for u → 0 than for large u and more trustworthy for antiparallel spins than for parallel spins. We illustrate how good LSD is as u = 0 with explicit examples, but also note that, contrary to expectation, LSD is not exact for u=0, except in certain limiting cases. We show that the dramatic failure of the second-order gradient expansion for large u can be cured by a real-space cutoff procedure which generates a nonempirical GGA, the Pw91 functional. We conclude with some thoughts about the search for greater accuracy in the next 30 years of density functional theory. © 1995 John Wiley & Sons, Inc.     

Computational study of analogues of the uranyl ion containing the -N=U=N- unit: density functional theory calculations on UO2(2+), UON+, UN2, UO(NPH3)3+, U(NPH3)2(4+), [UCl4[NPR3]2] (R = H, Me), and [UOCl4[NP(C6H5)3]

The electronic and geometric structures of the title species have been studied computationally using quasi-relativistic gradient-corrected density functional theory. The valence molecular orbital ordering of UO2(2+) is found to be pi g < pi u < sigma g < sigma u (highest occupied orbital), in agreement with previous experimental conclusions. The significant energy gap between the sigma g and sigma u orbitals is traced to the "pushing from below" mechanism: a filled-filled interaction between the semi-core uranium 6p atomic orbitals and the sigma u valence level. The U-N bonding in UON+ and UN2 is significantly more covalent than the U-O bonding in UON+ and UO2(2+). UO(NPH3)3+ and U(NPH3)2(4+) are similar to UO2(2+), UON+, and UN2 in having two valence molecular orbitals of metal-ligand sigma character and two of pi character, although they have additional orbitals not present in the triatomic systems, and the U-N sigma levels are more stable than the U-N pi orbitals. The inversion of U-N sigma/pi orbital ordering is traced to significant N-P (and P-H) sigma character in the U-N sigma levels. The pushing from below mechanism is found to destabilize the U-N f sigma molecular orbital with respect to the U-N d sigma level in U(NPH3)2(4+). The uranium f atomic orbitals play a greater role in metal-ligand bonding in UO2(2+), UN2, and U(NPH3)2(4+) than do the d atomic orbitals, although, while the relative roles of the uranium d and f atomic orbitals are similar in UO2(2+) and U(NPH3)2(4+), the metal d atomic orbitals have a more important role in the bonding in UN2. The preferred UNP angle in [UCl4(NPR3)2] (R = H, Me) and [UOCl4(NP(C6H5)3)]- is found to be close to 180 degrees in all cases. This preference for linearity decreases in the order R = Ph > R = Me > R = H and is traced to steric effects which in all cases overcome an electronic preference for bending at the nitrogen atom. Comparison of the present iminato (UNPR3) calculations with previous extended Hückel work on d block imido (MNR) systems reveals that in all cases there is little or no preference for linearity over bending at the nitrogen when R is (a) only sigma-bound to the nitrogen and (b) sterically unhindered. The U/N bond order in iminato complexes is best described as 3.     

AB initio calculation of the zero-field splittings of the X3Σg− and B3Πg,i states of the S2 molecule

The zero-field splitting of the ³Σ_g^? ground state of S₂ is computed employing MRD CI wavefunctions obtained in a series of AO basis sets. All one- and two-electron spin—orbit interactions are included in the theoretical treatment and results are obtained and compared using second-order perturbation theory techniques and a CI-type diagonalization procedure. The computed data are found to be in good agreement with experiment, including the dependence of the splitting parameter on vibrational quantum number, and are seen to be quite stable with respect to variations in the AO basis as well as the number of inner-shell core orbitals maintained doubly occupied in all Slater determinants employed in the theoretical treatment.     

Highly selective sorption of small unsaturated hydrocarbons by nonporous flexible framework with silver ion

Ag2[Cr3O(OOCC2H5)6(H2O)3]2[alpha-SiW12O40] [1] is a nonporous flexible ionic crystal composed of 2D-layers of polyoxometalates ([alpha-SiW12O40](4-)) and macrocations ([Cr3O(OOCC2H5)6(H2O)3](+)) stacking along the b-axis. The silver ions are located in the vicinity of the oxygen atoms of the polyoxometalates. The sorption amounts of small unsaturated hydrocarbons such as ethylene, propylene, n-butene, acetylene, and methyl acetylene into 1 are comparable to or larger than 1.0 mol mol(-1) and large hystereses are observed, while those of paraffins and larger unsaturated hydrocarbons are smaller than the adsorption on the external surface (<0.2 mol mol(-1)). Fine crystals of 1 exhibit ethylene/ethane and propylene/propane sorption ratios over 100 at 298 K and 100 kPa, and the values are larger by 1 order of magnitude among those reported. The results of sorption kinetics, in situ IR spectroscopy, single crystal X-ray crystallography, and in situ powder XRD studies show that small unsaturated hydrocarbons penetrate into the solid bulk of 1 through the pi-complexation with Ag(+). The sorption property of 1 is successfully applied to the collection of ethylene from the gas mixture of ethane and ethylene.     

Copolymerization of acetylene with ethylene in the presence of dibenzenetitanium(0)

The interaction between acetylene and dibenzenetitanium(0) at a room temperature results in the acetylene polymerization and its reduction to ethylene, ethane, and methane at the expense of H atoms of the acetylene molecule. The catalytically active species capable of copolymerizing acetylene with ethylene that are formed during the reaction or are added into the system originate from the interaction of dibenzenetitanium(0) with acetylene.     

Adsorptive Separation of Acetylene from Light Hydrocarbons by Mesoporous Iron Trimesate MIL‐100(Fe)

A reducible metal–organic framework (MOF), iron(III) trimesate, denoted as MIL‐100(Fe), was investigated for the separation and purification of methane/ethane/ethylene/acetylene and an acetylene/CO₂ mixtures by using sorption isotherms, breakthrough experiments, ideal adsorbed solution theory (IAST) calculations, and IR spectroscopic analysis. The MIL‐100(Fe) showed high adsorption selectivity not only for acetylene and ethylene over methane and ethane, but also for acetylene over CO₂. The separation and purification of acetylene over ethylene was also possible for MIL‐100(Fe) activated at 423 K. According to the data obtained from operando IR spectroscopy, the unsaturated Fe^III sites and surface OH groups are mainly responsible for the successful separation of the acetylene/ethylene mixture, whereas the unsaturated Fe^II sites have a detrimental effect on both separation and purification. The potential of MIL‐100(Fe) for the separation of a mixture of C₂H₂/CO₂ was also examined by using the IAST calculations and transient breakthrough simulations. Comparing the IAST selectivity calculations of C₂H₂/CO₂ for four MOFs selected from the literature, the selectivity with MIL‐100(Fe) was higher than those of CuBTC, ZJU‐60a, and PCP‐33, but lower than that of HOF‐3.     

Decomposition of nuclear magnetic resonance spin-spin coupling constants into active and passive orbital contributions

The theory of the J-OC-PSP (decomposition of J into orbital contributions using orbital currents and partial spin polarization) method is derived to distinguish between the role of active, passive, and frozen orbitals on the nuclear magnetic resonance (NMR) spin-spin coupling mechanism. Application of J-OC-PSP to the NMR spin-spin coupling constants of ethylene, which are calculated using coupled perturbed density functional theory in connection with the B3LYP hybrid functional and a [7s,6p,2d/4s,2p] basis set, reveal that the well-known pi mechanism for Fermi contact (FC) spin coupling is based on passive pi orbital contributions. The pi orbitals contribute to the spin polarization of the sigma orbitals at the coupling nuclei by mediating spin information between sigma orbitals (spin-transport mechanism) or by increasing the spin information of a sigma orbital by an echo effect. The calculated FC(pi) value of the SSCC (1)J(CC) of ethylene is 4.5 Hz and by this clearly smaller than previously assumed.     

Core localization and sigma* delocalization in the O 1s core-excited sulfur dioxide molecule

Electron-ion-ion coincidence measurements of sulfur dioxide at discrete resonances near the O 1s ionization edge are reported. The spectra are analyzed using a model based upon molecular symmetry and on the geometry of the molecule. We find clear evidence for molecular alignment that can be ascribed to symmetry properties of the ground and core-excited states. Configuration interaction (CI) calculations indicate geometry changes in accord with the measured spectra. For the SO(2) molecule, however, we find that the localized core hole does not produce measurable evidence for valence localization, since the transition dipole moment is not parallel to a breaking sigma* O-S bond, in contrast to the case of ozone. The dissociation behavior based upon the CI calculations using symmetry-broken orbitals while fixing a localized core-hole site is found to be nearly equivalent to that using symmetry-adapted orbitals. This implies that the core-localization effect is not strong enough to localize the sigma* valence orbital.     

A unified treatment of valence and bond order from density operators

A generalization of the quantum chemical definition of valence of atoms in molecules is suggested. Valence is considered as expectation value of diatomic parts of density operators. It appears as a sum of contributions from occupied orbitals of all atomic pairs that contain the reference atom. This definition is applicable on self-consistent-field (SCF ) and configuration interaction (CI ) level in any atomic orbitals (AO ) basis. Its usefulness is demonstrated in an application to special molecules. Photoelectron spectroscopy and reactivity is discussed in this context.     

Probing anisotropic interaction potentials of unsaturated hydrocarbons with He*(2 3S) metastable atom: attractive-site preference of sigma-direction in C2H2 and pi-direction in C2H4

State-resolved collision energy dependence of Penning ionization cross sections of acetylene (C2H2) and ethylene (C2H4) with He*(2 3S) metastable atoms was observed in a wide collision energy range from 20 to 350 meV. A recently developed discharge nozzle source with a liquid N2 circulator was employed for the measurements in the low-energy range from 20 to 80 meV. Based on classical trajectory calculations for the energy dependence of the partial ionization cross sections, anisotropic potential energy surfaces for the present systems were obtained by optimizing ab initio model potentials for the chemically related systems Li+C2H2 and C2H4. In the case of C2H2, the global minimum was found to be located around the H atom along the molecular axis with a well depth of 48 meV (ca. 1.1 kcal/mol). On the other hand, a dominant attractive well with a depth of 62 meV (ca. 1.4 kcal/mol) was found in the piCC electron region of C2H4. These findings were discussed in connection with orbital interactions between molecular orbitals of the target molecules and atomic orbitals of the metastable atom. It is concluded that sigma-type unoccupied molecular orbitals of C2H2 and a piCC-type highest occupied molecular orbital of C2H4 play a significant role for the attractive-site preference of sigma direction in C2H2 and pi direction in C2H4, respectively.     

Symmetry components analysis of nuclear spin–spin coupling constants

Molecular symmetry properties are used to define “normal” spin–spin coupling constants corresponding to some irreducible representations of the symmetry point group of the molecule. The relationship between these normal coupling constants and the measured ones is established in closed form for the most common cases. The Ramsey perturbation formula is analysed into symmetry components by means of the Winger–Eckart theorem. Both contributions predicted by the molecular-orbital method, i. e. direct coupling via σ electrons and indirect coupling via σ–π interaction are studied. Numerical calculations for the coupling constants of ethane, ethylene and acetylene were carried out without the mean excitation energy approximation by using SCF ? MO wave functions; overlap between atomic orbitals is systematically taken into account by calculating coupling constants. Theoretical and experimental results are compared in terms of symmetry components.     

Effect of addition of a graphitized carbon black trap to a glass beads trap on the cryoconcentration of some non-methane hydrocarbons in ambient air

Carbotrap was added to a glass beads cryotrap in order to increase the retention of the very volatile two-carbon hydrocarbons, ethylene, ethane and acetylene. Indeed the obtained recoveries increased from 2 to 3% for ethylene, the poorest retained compound, from 7 to 20% for ethane and from 23 to 31% for acetylene between the glass beads only and the Carbotrap/glass beads cryotrap. The addition of the Carbotrap, however, decreased the obtained recovery of o-xylene by 22–46%, depending on the employed conditions. The smaller decrease was observed when the longer desorption time was employed. The variation of the temperature of desorption by 40°C had very little effect on the resulting recoveries.     

Mixed valence—Rydberg states

A survey of recent calculations involving the mixing of Rydberg and valence states in the spectra of molecular systems is undertaken. It is pointed out that when such states undergo curve crossings with one another, minimal energy splittings of 1.0–2.0 eV can occur at the respective 50-50 composition points. The significance of such large interactions between valence and low-lying Rydberg states is considered in terms of the properties of the resulting mixed CI states, particularly with reference to the oscillator strengths for the pertinent ground state transitions and also the spatial extension of the corresponding upper orbitals. It is thereupon argued that such mixings have important consequences in the spectra of a wide variety of systems, including those of O₂, ethylene and ethane.