Low energy (e,2e) measurements of CH4 and neon in the perpendicular plane

Low energy experimental and theoretical triple differential cross sections for the highest occupied molecular orbital of methane (1t(2)) and for the 2p atomic orbital of neon are presented and compared. These targets are iso-electronic, each containing 10 electrons and the chosen orbital within each target has p-electron character. Observation of the differences and similarities of the cross sections for these two species hence gives insight into the different scattering mechanisms occurring for atomic and molecular targets. The experiments used perpendicular, symmetric kinematics with outgoing electron energies between 1.5 eV and 30 eV for CH(4) and 2.5 eV and 25 eV for neon. The experimental data from these targets are compared with theoretical predictions using a distorted-wave Born approximation. Reasonably good agreement is seen between the experiment and theory for neon while mixed results are observed for CH(4). This is most likely due to approximations of the target orientation made within the model.     

Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity

Orbital energies in Kohn-Sham density functional theory (DFT) are investigated, paying attention to the role of the integer discontinuity in the exact exchange-correlation potential. A series of closed-shell molecules are considered, comprising some that vertically bind an excess electron and others that do not. High-level ab initio electron densities are used to calculate accurate orbital energy differences, Deltavarepsilon, between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), using the same potential for both. They are combined with accurate vertical ionization potentials, I(0), and electron affinities, A(0), to determine accurate "average" orbital energies. These are the orbital energies associated with an exchange-correlation potential that averages over a constant jump in the accurate potential, of magnitude Delta(XC)=(I(0)-A(0))-Deltavarepsilon, as given by the discontinuity analysis. Local functional HOMO energies are shown to be almost an order of magnitude closer to these average values than to -I(0), with typical discrepancies of just 0.02 a.u. For systems that do not bind an excess electron, this level of agreement is only achieved when A(0) is set equal to the negative experimental affinity from electron transmission spectroscopy (ETS); it degrades notably when the zero ground state affinity is instead used. Analogous observations are made for the local functional LUMO energies, although the need to use the ETS affinities is less pronounced for systems where the ETS values are very negative. The application of an asymptotic correction recovers the preference, leading to positive LUMO energies (but bound orbitals) for these systems, consistent with the behavior of the average energies. The asymptotically corrected LUMO energies typically agree with the average values to within 0.02 a.u., comparable to that observed with the HOMOs. The study provides numerical support for the view that local functionals exhibit a near-average behavior based on a constant jump of magnitude Delta(XC). It illustrates why a recently proposed DFT expression involving local functional frontier orbital energies and ionization potential yields reasonable estimates of negative ETS affinities and is consistent with earlier work on the failure of DFT for charge-transfer excited states. The near-average behavior of the exchange-correlation potential is explicitly illustrated for selected systems. The nature of hybrid functional orbital energies is also mentioned, and the results of the study are discussed in terms of the variation in electronic energy as a function of electron number. The nature of DFT orbital energies is of great importance in chemistry; this study contributes to the understanding of these quantities.     

Understanding glycine conformation through molecular orbitals

The four most stable C(s) conformers of glycine have been investigated using a variety of quantum-mechanical methods based on Hartree-Fock theory, density-functional theory (B3LYP and statistical average of orbital potential), and electron propagation (OVGF) treatments. Information obtained from these models were analyzed in coordinate and momentum spaces using dual space analysis to provide insight based on orbitals into the bonding mechanisms of glycine conformers, which are generated by rotation of C-O(H) (II), C-C (III), and C-N (IV) bonds from the global minimum structure (I). Wave functions generated from the B3LYP/TZVP model revealed that each rotation produced a unique set of fingerprint orbitals that correspond to a specific group of outer valence orbitals, generally of a' symmetry. Orbitals 14a', 13a', 12a', and 11a' are identified as the fingerprint orbitals for the C-O(H) (II) rotation, whereas fingerprint orbitals for the C-C (III) bond rotation are located as 16a' [highest occupied molecular orbital (HOMO)], 15a' [next highest molecular occupied molecular orbital (NHOMO)], 14a', and 12a' orbitals. Fingerprint orbitals for IV generated by the combined rotations around the C-C, C-O(H), and C-N bonds are found as 16a', 15a', 14a', 13a', and 11a', as well as in orbitals 2a" and 1a". Orbital 14a' is identified as the fingerprint orbital for all three conformational processes, as it is the only orbital in the outer valence region which is significantly affected by the conformational processes regardless rotation of which bond. Binding energies, molecular geometries, and other molecular properties such as dipole moments calculated based on the specified treatments agree well with available experimental measurements and with previous theoretical calculation.     

CF2BrCl分子近域轨道的电子动量谱学研究

The frontier molecular orbitals (HOMO and NHOMO) of CF2BrCl molecule have been firstly investigated by (e,2e) electron momentum spectroscopy. The experimental momentum profiles are compared with the theoretical profiles employing Hartree-Fock and density functional theory with 6-31G and 6-311+G(d) basis sets. Both HF and DFT calculations using 6-311+G(d) basis set can well describe the experiment, whereas those calculated using 6-31G basis set largely underestimate the experiment at the low momentum region. Furthermore, orbital electron density images show that HOMO and NHOMO have a mixed character of the bromine and chlorine lone pairs.     

Ionization energy of atoms obtained from GW self-energy or from random phase approximation total energies

A systematic evaluation of the ionization energy within the GW approximation is carried out for the first row atoms, from H to Ar. We describe a Gaussian basis implementation of the GW approximation, which does not resort to any further technical approximation, besides the choice of the basis set for the electronic wavefunctions. Different approaches to the GW approximation have been implemented and tested, for example, the standard perturbative approach based on a prior mean-field calculation (Hartree-Fock GW@HF or density-functional theory GW@DFT) or the recently developed quasiparticle self-consistent method (QSGW). The highest occupied molecular orbital energies of atoms obtained from both GW@HF and QSGW are in excellent agreement with the experimental ionization energy. The lowest unoccupied molecular orbital energies of the singly charged cation yield a noticeably worse estimate of the ionization energy. The best agreement with respect to experiment is obtained from the total energy differences within the random phase approximation functional, which is the total energy corresponding to the GW self-energy. We conclude with a discussion about the slight concave behavior upon number electron change of the GW approximation and its consequences upon the quality of the orbital energies.     

Density functional study of structural and electronic properties of AlnN (1 ≤ n ≤ 12) clusters

Low‐lying equilibrium geometric structures of Al_nN (n = 1–12) clusters obtained by an all‐electron linear combination of atomic orbital approach, within spin‐polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three‐parameter hybrid generalized gradient approximation (GGA) due to Becke–Lee–Yang–Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground‐state structures within the GGA. It is observed that symmetric structures with the nitrogen atom occupying the internal position are lowest‐energy geometries. Generalized gradient approximation extends bond lengths as compared with the LSDA lengths. The odd–even oscillations in the dissociation energy, the second differences in energy, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energies clearly shows the Al₇N cluster to be endowed with special stability. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Koopmans' theorem for large molecular systems within density functional theory

It is shown that in density functional theory (DFT), Koopmans' theorem for a large molecular system can be stated as follows: The ionization energy of the system equals the negative of the highest occupied molecular orbital (HOMO) energy plus the Coulomb electrostatic energy of removing an electron from the system, or equivalently, the ionization energy of an N-electron system is the negative of the arithmetic average of the HOMO energy of this system and the lowest unoccupied molecular orbital (LUMO) energy of the (N - 1)-electron system. Relations between this DFT Koopmans' theorem and its existing counterparts in the literature are discussed. Some of the previous results are generalized and some are simplified. DFT calculation results of a fullerene molecule, a finite single-walled carbon nanotube and a finite boron nitride nanotube are presented, indicating that this Koopmans' theorem approximately holds, even if the orbital relaxation is taken into consideration.     

Experimental and theoretical (e,2e) ionization cross sections for a hydrogen target at 75.3 eV incident energy in a coplanar asymmetric geometry

Very recently it was shown that the molecular three-body distorted wave (M3DW) approach gives good agreement with the shape of the experimental data for electron-impact ionization of H(2) in a coplanar symmetric geometry, providing the incident electrons have an energy of 35 eV or greater. One of the weaknesses of these studies was that only the shape of the cross section could be compared to experiment, since there was no absolute or relative normalization of the data. Here we report a joint experimental/theoretical study of electron-impact ionization of H(2) in a coplanar asymmetric geometry where the energy of the incident electron was fixed, and different pairs of final state electron energies were used. In this case, the experimental data can be normalized such that only one renormalization factor is required. It is shown that the M3DW is pretty good in agreement with experiment. However, a better treatment of polarization and exchange between the continuum and bound state electrons is required before quantitative agreement between experiment and theory is achieved.     

Long‐range corrected functionals satisfy Koopmans' theorem: Calculation of correlation and relaxation energies

In this article, we show that the long‐range‐corrected (LC) density functionals LC‐BOP and LCgau‐BOP reproduce frontier orbital energies and highest‐occupied molecular orbital (HOMO)—lowest‐unoccupied molecular orbital (LUMO) gaps better than other density functionals. The negative of HOMO and LUMO energies are compared with the vertical ionization potentials (IPs) and electron affinities, respectively, using CCSD(T)/6‐311++G(3df,3pd) for 113 molecules, and we found LC functionals to satisfy Koopmans' theorem. We also report that the frontier orbital energies and the HOMO‐LUMO gaps of LC‐BOP and LCgau‐BOP are better than those of recently proposed ωM05‐D (Lin et al., J. Chem. Phys. 2012, 136 , 154109). We express the exact IP in terms of orbital relaxation, and correlation energies and hence calculate the relaxation and correlation energies for the same set of molecules. It is found that the LC functionals, in general, includes more relaxation effect than Hartree–Fock and more correlation effect than the other density functionals without LC scheme. Finally, we scan μ parameter in LC scheme from 0.1 to 0.6 bohr^?1 for the above test set molecules with LC‐BOP functional and found our parameter value, 0.47 bohr^?1, is usefully applicable to our tested systems. © 2013 Wiley Periodicals, Inc.     

Pulsed-field ionization zero electron kinetic energy spectrum of the ground electronic state of BeOBe+

The ground electronic state of BeOBe(+) was probed using the pulsed-field ionization zero electron kinetic energy photoelectron technique. Spectra were rotationally resolved and transitions to the zero-point level, the symmetric stretch fundamental and first two bending vibrational levels were observed. The rotational state symmetry selection rules confirm that the ground electronic state of the cation is (2)Σ(g)(+). Detachment of an electron from the HOMO of neutral BeOBe results in little change in the vibrational or rotational constants, indicating that this orbital is nonbonding in nature. The ionization energy of BeOBe [65480(4) cm(-1)] was refined over previous measurements. Results from recent theoretical calculations for BeOBe(+) (multireference configuration interaction) were found to be in good agreement with the experimental data.     

A quantum mechanical study of bioactive 3-chloro-2,5-dihydroxybenzyl alcohol through substitutions

Electronic structures, vibrational and ionization spectra of 3-chloro-2,5-dihydroxybenzyl alcohol (CHBA), a novel bioactive benzene derivative from marine fungi, are presented in this study using quantum mechanical methods such as density functional theory and outer valence Green function method. A number of related benzene derivatives such as chlorobenzene, 3-chlorobenzyl alcohol, hydroquinone and chlorohydroquinone are also studied, in order to assist our understanding of the structure, properties and interactions of CHBA. Vibrational spectra such as infrared (IR) and Raman spectra reveal signatures of the functional group substitutions and their hydrogen bond interactions in CHBA. Solvent effects on the IR spectra of CHBA with polar and non-polar solvents are simulated using the polarizable continuum model (PCM) and cause redshifts of some of the IR spectral frequencies with respect to the gas phase values at both ends of the 400?C4,000?cm^?1 region. The inner-shell ionization spectra, in particular the C?CK spectra of the benzene derivatives, reveal detailed chemical environmental changes of the carbon and oxygen atoms due to the substitutions. The valence ionization energies of the highest occupied molecular orbital (HOMO) and the 3rd HOMO, (HOMO-2) of the benzene derivatives respond significantly to the substitutions, whereas the charge distributions of the HOMO and 2nd HOMO (HOMO-1) do not change significantly from their benzene counterparts. As a result, the 3rd HOMO changes significantly in both ionization energies and the charge distributions, which can serve as a signature of the substitutions among the benzene derivatives.     

Excitation energies expressed as orbital energies of Kohn–Sham density functional theory with long-range corrected functionals

A new simple and conceptual theoretical scheme is proposed for estimating one-electron excitation energies using Kohn–Sham (KS) solutions. One-electron transitions that are dominated by the promotion from one initially occupied orbital to one unoccupied orbital of a molecular system can be expressed in a two-step process, ionization, and electron attachment. KS with long-range corrected (LC) functionals satisfies Janak's theorem and LC total energy varies almost linearly as a function of its fractional occupation number between the integer electron points. Thus, LC reproduces ionization energies (IPs) and electron affinities (EAs) with high accuracy and one-electron excitation energies are expressed as the difference between the occupied orbital energy of a neutral molecule and the corresponding unoccupied orbital energy of its cation. Two such expressions can be used, with one employing the orbital energies for the neutral and cationic systems, while the other utilizes orbital energies of just the cation. Because the EA of a molecule is the IP of its anion, if we utilize this identity, the two expressions coincide and give the same excitation energies. Reasonable results are obtained for valence and core excitations using only orbital energies.     

Vibrational state dependence of beta and D asymmetry parameters: the case of the highest occupied molecular orbital photoelectron spectrum of methyl-oxirane

The beta angular asymmetry and D dichroic asymmetry parameters of the methyl-oxirane highest occupied molecular orbital (HOMO) band have been experimentally investigated with vibrational resolution using synchrotron radiation. A theoretical calculation of the Franck-Condon factors between vibrational ground state and different ionic vibrational states, in the Born-Oppenheimer harmonic approximation, has been performed in order to gain information on the vibrational states mainly involved in the HOMO photoelectron band. The general good agreement between theoretical and experimental results allows a reliable assignment of the major features. The experimental determination of beta and D shows their dependence on the different final vibrational states. This paper reports, for the first time, experimental evidence of the dependence of the dichroic D parameter on the vibrational excitation of the ion.     

Quantum parameters based study of some heterocycles using density functional theory method: A comparative theoretical study

Density functional theory can envisage a vast assortment of molecular possessions such as molecular structures, vibrational frequencies, molecular energies, ionization energies, polar, electric and magnetic properties etc. The efficacy of this method relies on the study of electronic parameters to categorize the reactive sites to comprehend the plausible action of these scaffolds. Further it also facilitates the correlation between the structural characteristics of drug and their inhibition efficiency against infectious microorganisms. In light of the above facts, we have studied the structural parameters such as energy (total), variation of electron density over highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), charge distribution, absolute electronegativity (χ), softness/hardness (σ/ɳ) and fraction of electron transfer (ΔN) of some previously synthesized heterocycles.     

Control of emission by intermolecular fluorescence resonance energy transfer and intermolecular charge transfer

Control of emission by intermolecular fluorescence resonant energy transfer (IFRET) and intermolecular charge transfer (ICT) is investigated with the quantum-chemistry method using two-dimensional (2D) and three-dimensional (3D) real space analysis methods. The work is based on the experiment of tunable emission from doped 1,3,5-triphenyl-2-pyrazoline (TPP) organic nanoparticles (Peng, A. D.; et al. Adv. Mater. 2005, 17, 2070). First, the excited-state properties of the molecules, which are studied (TPP and DCM) in that experiment, are investigated theoretically. The results of the 2D site representation reveal the electron-hole coherence and delocalization size on the excitation. The results of 3D cube representation analysis reveal the orientation and strength of the transition dipole moments and intramolecular or intermolecular charge transfer. Second, the photochemical quenching mechanism via IFRET is studied (here "resonance" means that the absorption spectrum of TPP overlaps with the fluorescence emission spectrum of DCM in the doping system) by comparing the orbital energies of the HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital) of DCM and TPP in absorption and fluorescence. Third, for the DCM-TPP complex, the nonphotochemical quenching mechanism via ICT is investigated. The theoretical results show that the energetically lowest ICT state corresponds to a pure HOMO-LUMO transition, where the densities of the HOMO and LUMO are strictly located on the DCM and TPP moieties, respectively. Thus, the lowest ICT state corresponds to an excitation of an electron from the HOMO of DCM to the LUMO of TPP.     

Dynamical (e,2e) studies of tetrahydrofurfuryl alcohol

Cross section data for electron scattering from DNA are important for modelling radiation damage in biological systems. Triply differential cross sections for the electron impact ionization of the highest occupied outer valence orbital of tetrahydrofurfuryl alcohol, which can be considered as an analogue to the deoxyribose backbone molecule in DNA, have been measured using the (e,2e) technique. The measurements have been performed with coplanar asymmetric kinematics at an incident electron energy of 250 eV, an ejected electron energy of 20 eV, and at scattered electron angles of -5°, -10°, and -15°. Experimental results are compared with corresponding theoretical calculations performed using the molecular 3-body distorted wave model. Some important differences are observed between the experiment and calculations.     

Photoelectron spectroscopy and theoretical studies of UF5(-) and UF6(-)

The UF(5)(-) and UF(6)(-) anions are produced using electrospray ionization and investigated by photoelectron spectroscopy and relativistic quantum chemistry. An extensive vibrational progression is observed in the spectra of UF(5)(-), indicating significant geometry changes between the anion and neutral ground state. Franck-Condon factor simulations of the observed vibrational progression yield an adiabatic electron detachment energy of 3.82 ± 0.05 eV for UF(5)(-). Relativistic quantum calculations using density functional and ab initio theories are performed on UF(5)(-) and UF(6)(-) and their neutrals. The ground states of UF(5)(-) and UF(5) are found to have C(4v) symmetry, but with a large U-F bond length change. The ground state of UF(5)(-) is a triplet state ((3)B(2)) with the two 5f electrons occupying a 5f(z3)-based 8a(1) highest occupied molecular orbital (HOMO) and the 5f(xyz)-based 2b(2) HOMO-1 orbital. The detachment cross section from the 5f(xyz) orbital is observed to be extremely small and the detachment transition from the 2b(2) orbital is more than ten times weaker than that from the 8a(1) orbital at the photon energies available. The UF(6)(-) anion is found to be octahedral, similar to neutral UF(6) with the extra electron occupying the 5f(xyz)-based a(2u) orbital. Surprisingly, no photoelectron spectrum could be observed for UF(6)(-) due to the extremely low detachment cross section from the 5f(xyz)-based HOMO of UF(6)(-).     

(e,2e) Spectroscopy of methane

Measurements are reported on the spectroscopy of methane using the symmetric (e,2e) technique at energies of 600 eV and 1200 eV. The angular correlations of the states with separation energies of 14.2 and 23.1 eV have been measured and compared with the orbital wavefunctions of Snyder and Basch and with some earlier data at 400eV. The angular correlation of the configuration interaction state at 31 eV shows that this state definetely results from the removal of an electron in the 2a₁ orbital. Other structure at high separation energy is also identified with this orbital. Relative strengths of the It₂ and 2a₁ states are compared and found to be in agreement with the theory at 1200eV.     

The correlation of redox potential, HOMO energy, and oxidation state in metal sulfide clusters and its application to determine the redox level of the FeMo-co active-site cluster of nitrogenase

This paper describes a procedure that permits the total charge state (i.e., oxidation state) of a complex molecule to be obtained from its redox potential data by comparison with good data (both charge state and redox potential) for reference compounds that are chemically similar. The link between the reference data and the unknown compound is made by the calculated energies of the Fermi level or highest occupied molecular orbital (HOMO). The HOMO energies are calculated by unrestricted density functional methods (DMol) for the reference compounds in their known charge states, and a graphical correlation of HOMO energy and redox potential for oxidation (corresponding to loss of an electron from the HOMO) is constructed. The measured redox potential of the unknown is then applied to the correlation to yield the HOMO energy of the unknown, against which the calculated HOMO energies for various charge states of the unknown are assessed. This method is generally applicable. Using 26 reference data, the method is used here to determine the resting redox state, [NFe6MoS9]0, of the core of the FeMo cofactor (FeMo-co, bound to the MoFe protein) which is the active site of nitrogen-fixing enzymes. The analysis also shows that if the atom at the center of FeMo-co is C rather than N, then FeMo-co must be protonated in its resting state, but if FeMo-co is N-centered, it would not be protonated in the resting state.     

Biradicals stabilized by intramolecular charge transfer: properties of heterosubstituted pentalene and cyclooctatetraene biradicals

Intramolecular charge transfer can lead to substantial stabilization of singlet ground state and a corresponding increase of the singlet-triplet gap for molecules isoelectronic with the dianions of antiaromatic hydrocarbons. The formal biradicals 2,5-di-heterosubstituted-pentalenes and 1,5-di-heterosubstituted-cyclooctatetraenes are theoretically predicted to have the potential to be stable, persistent non-Kekulé molecules, as supported by high-level quantum chemical calculations. The singlet-triplet energy gaps and the S(0)-S(1) excitation energies of these molecules are similar to those of aromatic molecules rather than standard biradicals. These formal biradicals have a pronounced zwitterionic character, having a singlet ground state. The marked stabilization of the ground-state singlet for these non-Kekulé molecules is accompanied by a significant destabilization of the highest occupied molecular orbital (HOMO), leading to a low ionization potential (IP). This apparent inconsistency is explained by analyzing the electronic structure of the molecules. In the case of di-aza-pentalene, the energy of the first electronic excited state is only slightly lower than the ionization potential, making it a candidate for molecular autoionization.