The valence orbital momentum distributions and binding energy spectra of methane by electron momentum spectroscopy: Quantitative comparisons using near Hartree-Fock limit and correlated wavefunctions

Reference Energies for Valence Ionizations and Satellite Transitions

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.

Structural and dynamical studies of CH-πbonded CH4-C6H6dimer by ultrafast intermolecular Coulombic decay

The inner-valence ionization and fragmentation dynamics of CH₄-C₆H₆dimer induced by 200 eV electron impact is studied utilizing a multi-particle coincidence momentum spectroscopy. The three-dimensional momentum vectors and kinetic energy release (KER) of the CH₄⁺+C₆H₆⁺ion pairs are obtained by coincident momentum measurement. Our analysis on the absolute cross sections indicates that the intermediate dication CH₄⁺-C₆H₆⁺is preferentially produced by the removal of an inner-valence electron from CH₄or C₆H₆and subsequent relaxation of ultrafast intermolecular Coulombic decay followed by two-body Coulomb explosion. Combining withab initiomolecular dynamics (AIMD) simulations, the real-time fragmentation dynamics including translational, vibrational and rotational motions are presented as a function of propagation time. The revealed fragmentation dynamics are expected to have a potential implication for crystal structure imaging with various radiation sources.

Orbitals and the Interpretation of Photoelectron Spectroscopy and (e,2e) Ionization Experiments

Electron momentum spectroscopy, scanning tunneling microscopy, and photoelectron spectroscopy provide unique information about electronic structure, but their interpretation has been controversial. This essay discusses a framework for interpretation. Although this interpretation is not new, we believe it is important to present this framework in light of recent publications. The key point is that these experiments provide information about how the electron distribution changes upon ionization, not how electrons behave in the pre-ionized state. Therefore, these experiments do not lead to a "selection of the correct orbitals" in chemistry and do not overturn the well-known conclusion that both delocalized molecular orbitals and localized molecular orbitals are useful for interpreting chemical structure and dynamics. The two types of orbitals can produce identical total molecular electron densities and therefore molecular properties. Different types of orbitals are useful for different purposes.

An investigation of hybridization and the orbital models of molecular electronic structure for CH4, NH3, and H2O

Observations of the physical behaviour (motions) of the valence (frontier) electrons in the iconic benchmark hydride molecules CH4, NH3, and H2O are used to provide a direct experimental evaluation of hybridization and of the localized and delocalized orbital models of molecular electronic structure, after more than 80 years since the initial proposals of these theoretical concepts. Our previously published experimental measurements of valence (frontier) electron momentum probability distributions, made by electron momentum spectroscopy (EMS), are compared with those calculated using the localized molecular orbital (LMO) model and a range of hybrid orbital models, as well as with the delocalized canonical molecular orbital (CMO) and density functional theory Kohn–Sham orbital (KSO) models. In all cases, the electron momentum probability distributions calculated with LMOs and localized hybrid orbital type models are inconsistent with the experimental observations. In contrast, those calculated with the delocalized CMOs and KSOs are in very good agreement with the experimental measurements. These findings are of importance in those research applications such as reactivity, drug and novel material design, and also in molecular electronics, where the shapes and orientations of particular valence (frontier) orbital electron density probability distributions (and not the total electron densities) are considered to be key determining factors. These findings and their implications are also of pedagogical significance in chemistry and molecular physics.

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 signatures of methyl in L-alanine

Molecular orbital signatures of the methyl substituent in L-alanine have been identified with respect to those of glycine from information obtained in coordinate and momentum space, using dual space analysis. Electronic structural information in coordinate space is obtained using ab initio (MP2/TZVP) and density functional theory (B3LYP/TZVP) methods, from which the Dyson orbitals are simulated based on the plane wave impulse approximation into momentum space. In comparison to glycine, relaxation in geometry and valence orbitals in L-alanine is found as a result of the attachment of the methyl group. Five orbitals rather than four orbitals are identified as methyl signatures. That is, orbital 6a in the core shell, orbitals 11a and 12a in the inner valence shell, and orbitals 19a and 20a in the outer valence shell. In the inner valence shell, the attachment of methyl to glycine causes a splitting of its orbital 10a' into orbitals 11a and 12a of L-alanine, whereas in the outer valence shell the methyl group results in an insertion of an additional orbital pair of 19a and 20a. The frontier molecular orbitals, 24a and 23a, are found without any significant role in the methylation of glycine.

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.

Electron momentum spectroscopy of the frontier electrons of DABCO does not support ansp3hybrid lone-pair description

The highest occupied molecular orbital (HOMO) and next-highest occupied molecular orbital (NHOMO) valence orbital electron density distributions of 1,4-diazabicyclo[2.2.2]octane (DABCO) have been investigated by electron momentum spectroscopy, a technique that probes the orbital-like nature of valence (frontier) electron transfer out of a molecule. The experimental results are compared to a range of 6-311++G** calculations to assess the relative merits of three different orbital models that have commonly been used in chemistry. The delocalized (correlated) canonical Kohn–Sham orbitals calculated using the B3LYP or B3PW91 functionals and density functional theory provide near quantitative agreement with the observed valence electron momentum density distributions, and the delocalized canonical molecular orbitals of Hartree–Fock (independent particle) theory are in semiquantitative agreement. In contrast, Pauling's widely used and taught valence bond (hybridization) model, which is equivalent to a localized molecular orbital description, does not correspond at all to the experimental measurements. It follows that, for considerations of electron transfer, the "lone pairs" of DABCO are not localized or hybridized, but rather exist as nondegenerate orbitals that are delocalized differently over the molecular framework. The existence of two different experimental valence orbital electron densities of DABCO provides direct confirmation of the frontier orbital HOMO–NHOMO energy splitting and reordering predicted many years ago by Hoffmann et al. using extended Hückel theory, and interpreted in terms of "through bond" and "through space" interactions.Key words: orbitals, lone pairs, orbital interaction, hybridization.

Probing molecular conformations with electron momentum spectroscopy: the case of n-butane

High-resolution (e,2e) measurements of the valence electronic structure and momentum-space electron density distributions of n-butane have been exhaustively reanalyzed in order to cope with the presence of two stable structures in the gas phase, namely the all-staggered and gauche conformers. The measurements are compared to a series of Boltzmann-weighted simulations based on the momentum-space form of Kohn-Sham (B3LYP) orbital densities, and to ionization spectra obtained from high-level [ADC(3)] one-particle Green's Function calculations. Indubitable improvements in the quality of the simulated (e,2e) ionization spectra and electron momentum profiles are seen when the contributions of the gauche form of n-butane are included. Both the one-electron binding energies and momentum distributions consistently image the distortions and topological changes that molecular orbitals undergo due to torsion of the carbon backbone, and thereby exhibit variations which can be traced experimentally. With regard to the intimate relation of (e,2e) cross sections with orbital densities, electron momentum spectroscopy can therefore be viewed as a very powerful, but up to now largely unexploited, conformational probe. The study also emphasizes the influence of thermal agitation in photoionization experiments of all kind.

Orbitals observed by Electron Momentum Spectroscopy

Numerical representations of Dyson orbitals can be extracted from the experimental data of electron momentum spectroscopy (EMS). These orbitals are solutions of the quasiparticle equation for the target electronic system. They closely obey the weak-coupling approximation. This defines a normalized Dyson orbital in terms of the sum of EMS cross sections for an orbital manifold of ion states whose momentum profiles have the same shape. Normalized Dyson orbitals are closely related to the orbitals of density functional theory. They are realistic in the sense that they give an independent-particle approximation to the target structure that reproduces experimental data, including molecular data obtained from experiments independent of EMS.