Nonbonding Orbitals Research Articles

Interference effects on (e, 2e) electron momentum profiles: a comparative study for CCl4 and CF4*

Interference effects on electron momentum density distributions have been studied using electron momentum spectroscopy (EMS) for the three outermost orbitals of CCl4, which are constructed from the Cl 3p nonbonding atomic orbitals. The EMS experiment was conducted in the symmetric noncoplanar geometry at an incident electron energy of 2.0 keV. Interference pattern has then been obtained by dividing the experimental data by distorted-wave-Born-approximation cross section for an isolated Cl 3p atomic orbital. A comparison with the result of our earlier study on CF4 [N. Watanabe, X.-J. Chen, M. Takahashi, Phys. Rev. Lett. 108, 173201 (2012)] has demonstrated that the period of the interference pattern reflects the internuclear distance between the constituent halogen atoms. Furthermore, the present result strongly suggests that distorted-wave effects lead to partial destruction of the interference for CCl4 at large momentum.

Development of molecular fragment interaction method for designing organic ferromagnets

The design and preparation of organic ferromagnets are important and challenging from both experimental and theoretical viewpoints. We propose a molecular fragment interaction method for predicting the high-spin stability of conjugated hydrocarbon radicals without quantum chemistry calculations, which comprise three steps: (1) division of the system into fragments and numbering of the carbon atoms, (2) construction of a secular equation, and (3) solving of the secular equation. If there are two or more nonbonding molecular orbitals (NBMOs) and the smallest number of bonds between two carbon atoms with unpaired electrons is an even number, then the conjugated hydrocarbon radical has a high-spin ground state. This method can also be used to compare the high-spin stability between different conjugated hydrocarbon radicals. If a conjugated hydrocarbon radical has a high-spin ground state, then its derivative has a high-spin ground state as long as the degeneracy of the NBMOs is kept. This method is useful for the rapid design of organic ferromagnets.

Hg(II) Coordination Polymers Based on N,N'-bis(pyridine-4-yl)formamidine.

Reactions of N,N’-bis(pyridine-4-yl)formamidine (4-Hpyf) with HgX2 (X = Cl, Br, and I) afforded the formamidinate complex {[Hg(4-pyf)2]·(THF)}n, 1, and the formamidine complexes {[HgX2(4-Hpyf)]·(MeCN)}n (X = Br, 2; I, 3), which have been structurally characterized by X-ray crystallography. Complex 1 is a 2D layer with the {44·62}-sql topology and complexes 2 and 3 are helical chains. While the helical chains of 2 are linked through N–H···Br hydrogen bonds, those of 3 are linked through self-complementary double N–H···N hydrogen bonds, resulting in 2D supramolecular structures. The 4-pyf- ligands of 1 coordinate to the Hg(II) ions through one pyridyl and one adjacent amine nitrogen atoms and the 4-Hpyf ligands of 2 and 3 coordinate to the Hg(II) ions through two pyridyl nitrogen atoms, resulting in new bidentate binding modes. Complexes 1–3 provide a unique opportunity to envisage the effect of the halide anions of the starting Hg(II) salts on folding and unfolding the Hg(II) coordination polymers. Density function theory (DFT) calculation indicates that the emission of 1 is due to intraligand π→π * charge transfer between two different 4-pyf- ligands, whereas those of 2 and 3 can be ascribed to the charge transfer from non-bonding p-type orbitals of the halide anions to π * orbitals of the 4-pyf- ligands (n→π *). The gas sorption properties of the desolvated product of 1 are compared with the Cu analogues to show that the nature of the counteranion and the solvent-accessible volume are important in determining their adsorption capability.

Determination of the accurate ionization energy and cationic structure of cyanopyrazine by one-photon mass-analyzed threshold ionization spectroscopy

The ionization energy and cationic structure of cyanopyrazine have been determined for the first time by pulsed-field threshold ionization mass spectrometry. The ionization energy was accurately measured to be 80,305±6cm−1 (9.9566±0.0007eV) from the 0-0 band position in the mass-analyzed threshold ionization (MATI) spectrum obtained for the direct S0→D0 transition using a vacuum ultraviolet laser pulse generated by four-wave mixing in Kr. The highest occupied molecular orbital (HOMO) and singly occupied molecular orbital (SOMO) calculations indicated the extent of conjugation of nonbonding orbitals on nitrogen atoms with the π orbital in cyanopyrazine, and clarified the effect of substitution of H with CN in pyrazine on the ionization energy of cyanopyrazine. The observed MATI spectrum was interpreted using the Franck–Condon factors and vibrational frequencies calculated through adjustment of the geometrical parameters of the cyanopyrazine cation in the ground electronic state at the B3LYP/cc-pVTZ level. From rigorous analyses, it has been concluded that upon ionization, the cyanopyrazine cation in the D0 state should retain a planar structure with Cs symmetry, similar to the ground state molecule.

Electronic Excited States of the Dihalomethanes, \(\rm CH_2X_2 \ (X=Cl, Br, I)\)

The vacuum ultraviolet (VUV) photoabsorption spectra of the dihalomethanes \(\rm CH_2X_2 \ (X=Cl, Br, I)\) are studied using synchrotron radiation in the energy region 6–11.8 eV (\(\sim\)49,000–95,200 cm\(^{−1}\)). A detailed comparison is made to identify similarities, differences and trends in the spectra and excited state structure of these three molecules. The electronic spectra of the dihalomethanes in this region are dominated by Rydberg series of \(ns\), \(np\) and \(nd\) type. Quantum defect analysis reveals that the Rydberg series in all the dihalomethanes originate from the four outermost halogen lone pair non-bonding orbitals. On going from Cl to I, the energy difference between the first four ionization potentials decreases which as a consequence leads to spectral congestion and complications in spectral assignments. In all three molecules, several Rydberg transitions are accompanied by vibrational structure. A notable common feature seen in the vibronic structure is the excitation of the \(\nu_3\) (\(\rm C\)\(\rm -\)\(\rm X\) symmetric stretch) mode to form extensive progressions. Additionally, the \(\nu_1\) (\(\rm C\)\(\rm -\)\(\rm H\) symmetric stretch), \(\nu_2\) (\(\rm CH_2\) bend) and \(\nu_8\) (\(\rm CH_2\) wag) modes are observed in \(\rm CH_2Cl_2\) and \(\rm CH_2I_2\), although they do not form long progressions. Quantum chemical calculations of ground and excited states are used to support the analysis and an improved theory-experiment comparison is provided for \(\rm CH_2Br_2\).

Total π-Electron Energy of Conjugated Molecules with Non-bonding Molecular Orbitals

Abstract Lower and upper bounds for the total π-electron energy are obtained, which are applicable to conjugated π-electron systems with non-bonding molecular orbitals (NBMOs). These improve the earlier estimates, in which the number of NBMOs has not been taken into account.

Observation of Interference Effects in (e, 2e) Electron Momentum Spectroscopy of SF6

Two-dimensional electron density map (2D map) of binding energy and relative azimuthal angle (i.e., momentum) for the outer-valence molecular orbitals of SF6 has been measured by a highly sensitive electron momentum spectrometer with noncoplanar symmetric geometry at the impact energy of 1.2 keV plus binding energy. The experimental electron momentum profiles for the relevant molecular orbitals have been extracted from the 2D map and interpreted on the basis of the quantitative calculations using the density functional theory with B3LYP hybrid functional. For the outermost F2p nonbonding orbitals of SF6, the interference patterns are clearly observed in the ratios of the electron momentum profiles of molecular orbitals to that of atomic F2p orbital.

Atomic and electronic structures of Si(1 1 1)--Au and (6 × 6)-Au surfaces

Si(1 1 1)-Au surfaces with around one monolayer of Au exhibit many ordered structures and structures containing disordered domain walls. Hybrid density functional theory (DFT) calculations presented here reveal the origin of these complex structures and tendency to form domain walls. The conjugate honeycomb chain trimer (CHCT) structure of the -Au phase contains Si atoms with non-bonding surface states which can bind Au atoms in pairs in interstices of the CHCT structure and make this surface metallic. Si adatoms adsorbed on the -Au surface induce a gapped surface through interaction with the non-bonding states. Adsorption of extra Au atoms in interstitial sites of the -Au surface is stabilized by interaction with the non-bonding orbitals and leads to higher coverage ordered structures including the -Au phase. Extra Au atoms bound in interstitial sites of the -Au surface result in top layer Si atoms with an SiAu4 butterfly wing configuration. The structure of a -Au phase, whose in-plane top atomic layer positions were previously determined by an electron holography technique (Grozea et al 1998 Surf. Sci. 418 32), is calculated using total energy minimization. The Patterson function for this structure is calculated and is in good agreement with data from an in-plane x-ray diffraction study (Dornisch et al 1991 Phys. Rev. B 44 11221). Filled and empty state scanning tunneling microscopy (STM) images are calculated for domain walls and the -Au structure. The -Au phase is 2D chiral and this is evident in computed and actual STM images. -Au and domain wall structures contain the SiAu4 motif with a butterfly wing shape. Chemical bonding within the Si–Au top layers of the -Au and -Au surfaces is analyzed and an explanation for the SiAu4 motif structure is given.

A Comprehensive Analysis in Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. II. Strongly Correlated MCSCF Wave Functions.

A methodology is developed for the quantitative identification of the quasi-atomic orbitals that are embedded in a strongly correlated molecular wave function. The wave function is presumed to be generated from configurations in an internal orbital space whose dimension is equal to (or slightly larger) than that of the molecular minimal basis set. The quasi-atomic orbitals are found to have large overlaps with corresponding orbitals on the free atoms. They separate into bonding and nonbonding orbitals. From the bonding quasi-atomic orbitals, localized bonding and antibonding molecular orbitals are formed. The resolution of molecular density matrices in terms of these orbitals furnishes a basis for analyzing the interatomic bonding patterns in molecules and the changes in these bonding patterns along reaction paths. A new bond strength measure, the kinetic bond order, is introduced.

Covalent intermolecular interaction of the nitric oxide dimer (NO)2**Project supported by the National Natural Science Foundation of China (Grant Nos. 90403007 and 10975044), the Key Subject Construction Project of Hebei Provincial Universities, China, the Research Project of Hebei Education Department, China (Grant Nos. Z2012067 and Z2011133), the National Natural Science Foundation of China (Grant No. 11147103), and the Open Project

Covalent bonds arise from the overlap of the electronic clouds in the internucleus region, which is a pure quantum effect and cannot be obtained in any classical way. If the intermolecular interaction is of covalent character, the result from direct applications of classical simulation methods to the molecular system would be questionable. Here, we analyze the special intermolecular interaction between two NO molecules based on quantum chemical calculation. This weak intermolecular interaction, which is of covalent character, is responsible for the formation of the NO dimer, (NO)2, in its most stable conformation, a cis conformation. The natural bond orbital (NBO) analysis gives an intuitive illustration of the formation of the dimer bonding and antibonding orbitals concomitant with the breaking of the π bonds with bond order 0.5 of the monomers. The dimer bonding is counteracted by partially filling the antibonding dimer orbital and the repulsion between those fully or nearly fully occupied nonbonding dimer orbitals that make the dimer binding rather weak. The direct molecular mechanics (MM) calculation with the UFF force fields predicts a trans conformation as the most stable state, which contradicts the result of quantum mechanics (QM). The lesson from the investigation of this special system is that for the case where intermolecular interaction is of covalent character, a specific modification of the force fields of the molecular simulation method is necessary.

Symmetry breaking in the axial symmetrical configurations of enolic propanedial, propanedithial, and propanediselenal: pseudo Jahn–Teller effect versus the resonance-assisted hydrogen bond theory

The origin of the symmetry breaking in the axial symmetrical configurations of enolic propanedial (1), propanedithial (2), and propanediselenal (3) have been investigated by means of time-dependence density functional theory and natural bond orbital interpretations. The results obtained at the quantum chemistry composite (G2MP2, CBS-QB3), ab initio molecular orbital (MP2/6-311++G**), and hybrid density functional theory (B3LYP/6-311++G**) levels of theory showed that the hydrogen-centered synchronous axial symmetrical (C2v) configurations of compounds 1–3 possessing the maximum π-electron delocalization within the M1=C2–C3=C4–M5–H6 keto-enol groups are less stable than their corresponding plane symmetrical (Cs) forms. Importantly, the symmetry breaking in the C2v configurations of the enol forms of compounds 1–3 to their corresponding plane symmetrical Cs configurations is due to the pseudo Jahn–Teller effect (PJTE) by mixing the ground A1 and excited B2 electronic states resulting in a PJT (A1 + B2) ⊗ b2 problem. We may expect that by the decrease of the energy gaps between reference states in the C2v forms that are involved in the PJTE decrease from compound 1 to compound 3, the PJT stabilization energy (PJTSE) may increase but the results obtained showed that the corresponding PJTSEs decrease. This fact can be justified by the increase of the electron delocalizations from the nonbonding orbitals of the C=M moieties to the antibonding orbitals of the H–M bonds, which leads to an increase of the π-electron delocalization within the M1=C2–C3=C4–M5–H6 keto-enol groups. In confrontation between the impacts of the resonance-assisted hydrogen bond and PJTE in the structural and configurational properties of compounds 1–3, PJTE has an overwhelming contribution and causes the symmetry breaking of the C2v configurations to their corresponding Cs forms. The correlations between the structural parameters, synchronicity indices, natural charges, PJTSEs, electron delocalizations, and the hardness of compounds 1–3 have been investigated.

Unusual Tautomeric Energetics in 4n Azaheterocycles

Abstract Unusual imino preference in 4n azaheterocycles is theoretically analyzed. It is attributed to less topological charge stability of the amino forms due to antisymmetric nonbonding molecular orbitals. The theory is applicable for designing stable imino species. The same analysis is also applicable for hydroxyl/oxo tautomerism, and results in very stable lactams.

Development of minimized mixing molecular orbital method for designing organic ferromagnets.

Predicting the high spin stability of organic radicals correctly for designing organic ferromagnets remains a significant challenge. We have developed a method with an index (L(min)) for predicting the high spin stability of conjugated organic radicals at the restricted open-shell Hartree-Fock level. Unitary transformations were performed for localizing the coefficients of nonbonding molecular orbitals, and subsequently the localized coefficients were used to calculate L(min) that indicates the high spin stability of conjugated organic radicals. This method can be combined with the elongation method to treat huge high spin open-shell systems. Thus, this method is useful for designing organic ferromagnets.

Defect formation on the GaSb (001) surface induced by hydrogen atom adsorption

Density functional theory has been used to characterize the effects of adsorbed H on the electronic structure of the GaSb (001)-α(4×3) surface, which consists of a combination of Ga-Sb and Sb-Sb dimers. Adsorption of two H atoms at a Ga-Sb adatom dimer either has little effect on surface states above the bulk valence band maximum (VBM) or else eliminates them, depending on the mode of adsorption. However, adsorption at the Sb-Sb dimer in the terminating layer produces a state farther into the gap at ~0.10eV above the clean-surface VBM. Relaxation accompanying the breaking of the Sb-Sb dimer bond leads to increased interactions involving three-fold-coordinated Sb sites in the terminating layer, which in turn raises the energies of the non-bonding lone-pair orbitals. This defect state, which appears to be unique to the reconstructed GaSb (001) surface, could potentially function as a hole trap on the surface of p-type GaSb.

Conduction of molecular electronic devices: qualitative insights through atom-atom polarizabilities.

The atom-atom polarizability and the transmission probability at the Fermi level, as obtained through the source-and-sink-potential method for every possible configuration of contacts simultaneously, are compared for polycyclic aromatic compounds. This comparison leads to the conjecture that a positive atom-atom polarizability is a necessary condition for transmission to take place in alternant hydrocarbons without non-bonding orbitals and that the relative transmission probability for different configurations of the contacts can be predicted by analyzing the corresponding atom-atom polarizability. A theoretical link between the two considered properties is derived, leading to a mathematical explanation for the observed trends for transmission based on the atom-atom polarizability.

Electronic properties of fluorinated/semi-fluorinated boron–carbon monolayer: A first-principles study

Boron–carbon monolayer, a graphene-like sheet, attracts tremendous interests of theoretical and experimental researchers. Based on first-principle studies, we investigate the electronic and magnetic properties of fluorinated and semi-fluorinated BC3, BC5, BC7 and boron-doped graphene sheets. The results show that semiconductor–metal–semiconductor transitions appear in pure, fluorinated and semi-fluorinated BC3 sheet. BC5 and B-doped graphene sheets have metallic properties no matter they are fluorinated or semi-fluorinated. Semi-fluorinated BC7 sheet becomes to be a spin semiconductor and B-doped graphene sheet also has magnetic moments after semi-fluorination. We find that magnetism mainly originates from the non-bonding pz orbitals of unfluorinated carbon atoms, and boron atoms have an influence on the magnetic moments of compounds. Our studies demonstrate that the fluorination and semi-fluorination are effective routes to make electronic and magnetic transitions in the boron–carbon monolayer.

Magnetic properties and electronic structures of Ar3U(IV)–L Complexes with Ar = C5(CH3)4H(–) or C5H5(–) and L = CH3, NO, and Cl.

Electronic structures and magnetic properties of the U(4+) complexes (C5Me4H)3UNO, (C5Me4H)3UCl, (C5H5)3UCH3, and (C5H5)3UCl are investigated by quantum chemical calculations. On the basis of wave function calculations including spin-orbit (SO) interactions, all complexes have nondegenerate nonmagnetic ground states. However, for L = CH3 and Cl magnetic doublet excited states are very low in energy, rendering the magnetic susceptibility strongly temperature dependent above ca. 50-100 K. In contrast, (C5Me4H)3UNO exhibits temperature-independent paramagnetism even at room temperature. The calculated susceptibilities agree well with available experimental data. An analysis of the ground states and the magnetic behavior is performed using crystal-field (CF) models with parameters extracted from the ab initio calculations, and with the help of natural orbitals contributing to the electron density, generated from scalar relativistic and SO wave functions for the ground states and selected excited states. Electronic g-factors calculated from the CF models agree well with ab initio data. The U-NO bond order in (C5Me4H)3UNO decreases somewhat due to SO coupling, because U-NO bonding π orbitals with strong U 5fπ character mix with nonbonding 5fδ orbitals under the SO interaction. This complex also exhibits pronounced multireference character. All complexes afford U-ligand 5f covalent character.

Electronic states of carbon disulphide in the 5.5–11.8 eV region by VUV photo absorption spectroscopy

The photo absorption spectrum of carbon disulphide (CS2) is recorded using synchrotron radiation in the 5.5–11.8eV region. The richly structured spectrum of CS2 consists of valence and Rydberg transitions up to the first ionization potential (IP) at ~10.1eV and a few discrete peaks above the first IP. The low lying electronic states of CS2 are assigned to the singlet or triplet states originating from {2πg→3πu, 7σg, 8σg, 6σu, 4πu, 3πg, 9σg}, {2πu→3πu, 7σg} and {5σu→3πu} excitations. Rydberg series of type nlλ(l=s, p, d, f and λ=σ,π,δ,ϕ) are observed along with associated vibronic structure in a few low lying members. The derived quantum defect values for the s(~2.0), p(~1.6), d(~0.4) and f(~0.1) Rydberg states are consistent with excitation from sulphur non-bonding orbitals. The comprehensive experimental work presented here and the revisit of the study of electronic spectrum of CS2 gives a clearer picture of the nature and origin of various transitions and helps in interpreting several unassigned peaks. The vibrational features observed above the first IP are attributed to autoionization from a high lying Rydberg state. Theoretical calculations using the time dependent density functional theory method assists in evaluating vertical excitation energies, nature of the transitions and confirming or suggesting electronic assignments of a few low lying valence transitions where ambiguity existed.

Vacuum ultraviolet photoabsorption spectroscopy of CH2Cl2 and CD2Cl2 in the energy region 50,000–95,000 cm−1

A consolidated study of the VUV absorption spectra of CH2Cl2 and CD2Cl2 in the 50,000–95,000cm−1 region using synchrotron radiation is presented. Rydberg series and vibronic analysis are carried out and supported by quantum chemical calculations. The broad absorption band of CH2Cl2 in the region 50,000–60,000cm−1 is attributed to the valence states 11B2, 11B1 and 11A1. Most of the bands in the 60,000–95,000cm−1 region are fitted to Rydberg series of ns, np and nd type converging to the first four ionization potentials 11.320, 11.357, 12.152 and 12.271eV of CH2Cl2 arising from excitation of an electron from one of the four outermost Cl non-bonding orbitals (2b1, 3b2, 1a2 and 4a1). Vertical excited states of CH2Cl2 calculated using TDDFT are correlated with experimentally observed electronic states based on the symmetries of the initial and final MOs involved in a transition. A few Rydberg transitions viz. 2b1→5s, 4p, 5p, 6p; 3b2→4p, 5p; 1a2→4p are accompanied by vibronic features. Observed vibronic bands are assigned mainly to the CCl symmetric stretch (ν3′) mode with smaller contributions from the CH symmetric stretch (ν1′), CH2 bend (ν2′) and CH2 wag (ν8′) modes. Assignments are corroborated by comparison with the VUV absorption spectrum of the deuterated isotopologue CD2Cl2, reported here for the first time. The high underlying intensities seen in several sub-regions are explained by valence or valence–Rydberg mixed type transitions predicted with high oscillator strengths by the TDDFT calculations.

Magnetic properties and electronic structure of neptunyl(VI) complexes: wavefunctions, orbitals, and crystal-field models.

The electronic structure and magnetic properties of neptunyl(VI), NpO2(2+), and two neptunyl complexes, [NpO2(NO3)3](-) and [NpO2Cl4](2-), were studied with a combination of theoretical methods: ab initio relativistic wavefunction methods and density functional theory (DFT), as well as crystal-field (CF) models with parameters extracted from the ab initio calculations. Natural orbitals for electron density and spin magnetization from wavefunctions including spin-orbit coupling were employed to analyze the connection between the electronic structure and magnetic properties, and to link the results from CF models to the ab initio data. Free complex ions and systems embedded in a crystal environment were studied. Of prime interest were the electron paramagnetic resonance g-factors and their relation to the complex geometry, ligand coordination, and nature of the nonbonding 5f orbitals. The g-factors were calculated for the ground and excited states. For [NpO2Cl4](2-), a strong influence of the environment of the complex on its magnetic behavior was demonstrated. Kohn-Sham DFT with standard functionals can produce reasonable g-factors as long as the calculation converges to a solution resembling the electronic state of interest. However, this is not always straightforward.