Rydberg Orbitals Research Articles

Ultrafast dynamics of water system under photoexcitation

<sec>Experimental techniques and theoretical calculations have made significant breakthroughs recently in realizing the ultrafast time resolution and the understanding of microscopic details on an atomic scale, which has brought new insights into the ultrafast microscopic dynamics of water system and aqueous system. Here we focus on the dynamic processes of ionization, dissociation, as well as plasmonization of water molecules, water clusters, and liquid water under different intensities of light excitation.</sec><sec>The pump-probe technique allows one to extract the information about the orbital-dependent phase shift during photoionization, corresponding to delays on a time scale from tens to hundreds of attoseconds. Delay time in photoionization is found to be proportional to the delocalization of molecular/cluster orbitals. In addition, the information related to the Feshbach resonance is also of interest. By solving the scattering equations, the detailed information about the scattering cross section, the <i>β</i>-parameter, and the involved Rydberg orbitals during valence electron ionization of water is obtained.</sec><sec>For liquid water undergoing irradiation by an optical field, the tunneling electrons are unable to move away and recombine with the parent molecule on a time scale of 100 fs if the external field is not strong enough (e.g. ~100 kV/cm). For terahertz fields as high as 250 kV/cm, electrons will move away from the parent molecule after tunnelling and undergo decoherence on a 10-fs time scale. At the beginning of tunneling the electrons will be more delocalized and will collapse to a certain position on a time scale of ~1 ps, and then slowly diffuse or recombine with holes on a longer time scale. For the strong excitation case, hot electrons may also be formed. When a hot electron is located on a particular water molecule, the O—H bond will be broken.</sec><sec>When an electron ionizes away, a hole will be created. The hole will be located on a water molecule within 10 fs, and will trigger off subsequent processes such as proton transfer and coherent oscillations. In particular, after the hole is localized and before the proton is transferred, there is a brief appearance of the metastable <inline-formula><tex-math id="M1">\begin{document}$ {{{\mathrm{H}}}_{2}{\mathrm{O}}}^{+} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20240047_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20240047_M1.png"/></alternatives></inline-formula> ion, whose lifetime is experimentally captured and is predicted to be (46±10) fs. The nuclear quantum effect in this process plays a key role.</sec><sec>Using the methods such as real time-time dependent density functional theory (rt-TDDFT), it is found that the water undergoes plasmonization under intense laser pulses corresponding to a field strength amplitude larger than 2.4 V/Å. The effective electron temperature in this period reaches over 20000 K. Strongly excited water in this state exhibits the behaviors of a liquid metal, and extremely strong nonthermal effect and nonadiabatic effect. In the process of plasmonization, a large fraction of chemical bonds in water molecules are broken and reorganize themselves, and many chemical species such as hydrogen molecules may appear, which also implies that laser-induced plasmonization can be used to synthesize new substances.</sec><sec>Although the previous researches have brought about a very rich understanding, we have also found some details that still need to be explored: i) the influence of nuclear quantum effects has not been taken into account in most of theoretical calculations, which may result in the inadequate description and inaccurate prediction; ii) some of the microscopic details observed in simulations do not yet have a direct counterpart in experimental measurements; iii) the current simulation of water plasmonization is for the local behavior under the spatially uniform external field, while in the real situation there are spatial inhomogeneity and energy flow, which urgently need larger-scale excited state dynamics simulations.</sec><sec>With the development of laser technology, the integration of water science and ultrafast technologies will be increasingly strong, so we believe that such a systematic understanding will play a key role in the future. It is expected that new research efforts will continue to contribute to a better understanding and the generation of new technologies in this exciting research field.</sec>

Orbital-optimized density functional calculations of molecular Rydberg excited states with real space grid representation and self-interaction correction.

Density functional calculations of Rydberg excited states up to high energy are carried out for several molecules using an approach where the orbitals are variationally optimized by converging on saddle points on the electronic energy surface within a real space grid representation. Remarkably good agreement with experimental estimates of the excitation energy is obtained using the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof (PBE) when Perdew-Zunger self-interaction correction is applied in combination with complex-valued orbitals. Even without the correction, the PBE functional gives quite good results despite the fact that corresponding Rydberg virtual orbitals have positive energy in the ground state calculation. Results obtained using the Tao, Perdew, Staroverov, and Scuseria (TPSS) and r2SCAN meta-GGA functionals are also presented, but they do not provide a systematic improvement over the results from the uncorrected PBE functional. The grid representation combined with the projector augmented-wave approach gives a simpler and better representation of diffuse Rydberg orbitals than a linear combination of atomic orbitals with commonly used basis sets, the latter leading to an overestimation of the excitation energy due to confinement of the excited states.

Twin-Capture Rydberg State Excitation Enhanced with Few-Cycle Laser Pulses

Quantum excitation is usually regarded as a transient process occurring instantaneously, leaving the underlying physics shrouded in mystery. Recent research shows that Rydberg-state excitation with ultrashort laser pulses can be investigated and manipulated with state-of-the-art few-cycle pulses. We theoretically find that the efficiency of Rydberg state excitation can be enhanced with a short laser pulse and modulated by varying the laser intensities. We also uncover new facets of the excitation dynamics, including the launching of an electron wave packet through strong-field ionization, the re-entry of the electron into the atomic potential and the crucial step where the electron makes a U-turn, resulting in twin captures into Rydberg orbitals. By tuning the laser intensity, we show that the excitation of the Rydberg state can be coherently controlled on a sub-optical-cycle timescale. Our work paves the way toward ultrafast control and coherent manipulation of Rydberg states, thus benefiting Rydberg-state-based quantum technology.

Rydberg-type electronic excited state dynamics in small sodium–water clusters

Equilibrium geometries and thermodynamic potentials of the neutral and ionised species of the Na ⋯ ( H 2 O ) n ( n = 1 , . . , 8 ) mixed clusters were computed at MN15/def2-TZVPD level of density functional theory (DFT). The vertical and adiabatic ionisation energies and enthalpies were computed and their cluster size dependence was discussed. Laser-induced ionisation involves electronic excitation through Rydberg-type excited states, which have been characterised using the TDDFT method, including the ωB2PLYP double-hybrid exchange-correlation functional. Ab initio molecular dynamics calculations were performed on a time scale of 20 picoseconds. Fluctuations of the charge and the sodium–oxygen atomic distances predict that, the 3 s 1 electron of the sodium atom are transferred from the delocalised Rydberg orbitals to the Rydberg orbitals around the water molecules and the sodium atom becomes positively charged with around 0.6e after the first 10 ps . On the other hand, some of the water molecules can move away up to 5 Å from the sodium with a significant negative charge on them. It has been shown that non-radiative relaxation cannot be excluded, they can mostly occur for cases n ⩾ 4 . The results confirm that the adiabatic photo-ionisation can occur on the basis of cluster disintegration.

Measuring autoionization decay lifetimes of optically forbidden inner valence excited states in neon atoms with attosecond noncollinear four-wave-mixing spectroscopy

Attosecond noncollinear four wave mixing spectroscopy with one attosecond extreme ultraviolet (XUV) pulse and two few-cycle near-infrared (NIR) pulses was used to measure the autoionization decay lifetimes of inner valence electronic excitations in neon atoms. After a 43-48 eV XUV photon excites a 2s electron into the 2s2p6[np] Rydberg series, broadband NIR pulses couple the 2s2p6[3p] XUV-bright state to neighboring 2s2p6[3s] and 2s2p6[3d] XUV-dark states. Controllable delays of one or both NIR pulses with respect to the attosecond XUV pulse reveal the temporal evolution of either the dark or bright states, respectively. Experimental lifetimes for the 3s, 3p, and 3d states are measured to be 7 +/- 2 fs, 48 +/- 8 fs, and 427 +/- 40 fs, respectively, with 95% confidence. Accompanying calculations with two independent ab initio theoretical methods, NewStock and ASTRA, verify the findings. The results support the expected trend that the autoionization lifetime should be longer for states that have a smaller penetration in the radial region of the 2s core hole, which in this case is for the higher angular momentum Rydberg orbitals. The underlying theory thus links the lifetime results to electron correlation and provides an assessment of the direct and exchange terms in the autoionization process.

The Importance of Tight f Basis Functions for Heavy p-Block Oxides and Halides: A Parallel With Tight d functions in the Second Row.

It is well-known that both wave function ab initio and DFT calculations on second-row compounds exhibit anomalously slow basis set convergence unless the basis sets are augmented with additional "tight" (high-exponent) d functions, as in the cc-pV(n+d)Z and aug-cc-pV(n+d)Z basis sets. This has been rationalized as being necessary for a better description of the low-lying 3d orbital, which as the oxidation state increases sinks low enough to act as a back-donation acceptor from chalcogen and halogen lone pairs. This prompts the question whether a similar phenomenon exists for the isovalent compounds of the heavy p-block. We show that for the fourth and fifth row, this is the case, but this time for tight f functions enhancing the description of the low-lying 4f and 5f Rydberg orbitals, respectively. In the third-row heavy p block, the 4f orbitals are too far up, while the 4d orbitals are adequately covered by the basis functions already present to describe the 3d subvalence orbitals.

Introducing MPEC: Massively parallel electron correlation.

We have developed a new program for carrying out improved internally contracted Multi-reference Configuration Interaction Singles and Doubles (i2cMRCISD) calculations. It is designed from the ground up to be used on distributed memory parallel computers. Tests show good scaling properties with the number of cores per node and the number nodes. This program features Gaussian basis sets with ℓ > 6; scalar special relativity via the spin-free method; convergence to C∞v, D∞v, or spherical electronic states; special code to determine Rydberg orbitals; both uncontracted and contracted MRCISD wavefunctions; one and two electron properties, including full spin-orbit matrix elements with the Breit interaction; analytic calculation of Born-Oppenheimer diagonal correction for multi-configuration Hartree-Fock wavefunctions; and analytic calculation of second order Born-Oppenheimer corrections for Hartree-Fock wavefunctions. The program can be obtained from software.nasa.gov.

Role of Spin-Orbit Coupling in High-Order Harmonic Generation Revealed by Supercycle Rydberg Trajectories.

High-harmonic generation is typically thought of as a sub-laser-cycle process, with the electron's excursion in the continuum lasting a fraction of the optical cycle. However, it was recently suggested that long-lived Rydberg states can play a particularly important role in high harmonic generation by atoms driven by the combination of the counterrotating circularly polarized fundamental light field and its second harmonic. Here we report direct experimental evidence of very long and stable Rydberg trajectories contributing to high-harmonic generation in such fields. We track their dynamics inside the laser pulse using the spin-orbit evolution in the ionic core, utilizing the spin-orbit Larmor clock. We confirm their effect on harmonic emission both via microscopic simulations and by showing how this radiation can lead to a well-collimated macroscopic far-field signal. Our observations contrast sharply with the general view that long-lived Rydberg orbits should generate negligible contribution to the macroscopic far-field high harmonic response of the medium.

Dynamics of atoms within atoms

Recent experiments with Bose–Einstein condensates have entered a regime in which thousands of ground-state condensate atoms fill the Rydberg-electron orbit. After the excitation of a single atom into a highly excited Rydberg state, scattering off the Rydberg electron sets ground-state atoms into motion, such that one can study the quantum-many-body dynamics of atoms moving within the Rydberg atom. Here we study this many-body dynamics using Gross–Pitaevskii and truncated Wigner theory. Our simulations focus in particular on the scenario of multiple sequential Rydberg excitations on the same rubidium condensate which has become the standard tool to observe quantum impurity dynamics in Rydberg experiments. We investigate to what extent such experiments can be sensitive to details in the electron–atom interaction potential, such as the rapid radial modulation of the Rydberg molecular potential, or p-wave shape resonance. We demonstrate that both effects are crucial for the initial condensate response within the Rydberg orbit, but become less relevant for the density waves emerging outside the Rydberg excitation region at later times. Finally we explore the local dynamics of condensate heating. We find that it provides only minor corrections to the mean-field dynamics. Combining all these insights, our results suggest Bose–Einstein condensates as a viable platform for the in situ and real time interrogation of ultra-cold chemistry dynamics involving Rydberg states.

Finding Valence Antibonding Levels while Avoiding Rydberg, Pseudo-continuum, and Dipole-Bound Orbitals.

Electronic structure methods are now widely used to assist in the interpretation of many varieties of experimental data. The energies and physical characteristics (e.g., sizes, shapes, and spatial localization) of valence antibonding π* and σ* orbitals play key roles in a variety of chemical processes including photochemical reactions and electron attachment reductions and are used in Woodward-Hoffmann-type analyses to probe reaction energy barriers and energy surface intersections leading to internal conversion or intersystem crossings. One's ability to properly populate such valence antibonding orbitals within electronic structure calculations is often hindered by the presence of other molecular orbitals having similar energies. These intruding orbitals can be of Rydberg, pseudo-continuum, or dipole-bound characteristic. This article shows how, within the most widely available electronic structure codes, one can avoid the pitfalls presented by these intruding orbitals to properly populate a valence π* or σ* orbital and how to subsequently use that orbital in a calculation that includes electron correlation effects and thereby offers the possibility of chemically useful precision. Special emphasis is given to cases in which the electronic state is metastable.

The main factor determining the low inversion barriers of N-sulfenylimines

The energy and electronic parameters of the nitrogen atom inversion in isoelectronic N-alkylimines and N-sulfenylimines (H2C=NR, where R=Me, Et, SH, SMe) have been calculated using DFT method (B3LYP/6-311+G(d,p)) in terms of NBO. It has been established that substitution of methylene group by sulfur atom does not lead to the decrease in the inversion barriers due to the nN*S–H(С) interactions, since total energies of the nN*S–H(С), nNS–H(С) and nNnS interactions in the N-sulfenylimines and of the nN*С–H(С), nNС–H(С) interactions in the N-alkylimines are almost equal. The interactions of the nitrogen lone pair with the Rydberg orbitals of the sulfur atom (nNRY*S) promote the reduction of the inversion barriers of the N-sulfenylimines (by 28–33 kJ•mol–1) in comparison with the N-alkylimines. However, analysis of the total energies of all donor-acceptor and repulsive interactions between the nitrogen lone pair and the orbitals of neighboring atoms and bonds showed that they promote the increase in the inversion barriers of the N-sulfenylimines by 0.8–14.3 kJ•mol–1. The nS*C=N and nS*C=N interactions are the main factor that determines the decrease in the inversion barriers of the N-sulfenylimines relative to the N-alkylimines. These interactions, taking into account the corresponding interactions in the N-alkylimines, contribute to the barriers decrease of 64.5–71.7 kJ•mol–1.

Geometry, absorption and luminescence of small Ar clusters

We investigate the lowest excitonic levels of small argon clusters, , by means of the Hole-Particle Pseudopotential (HPP) formalism introduced by Dupláa and Spiegelmann. This formalism allows us to model the excited states associated to Rydberg orbitals with higher accuracy than previous studies based on the Diatomics-In-Molecule (DIM) approach, as used by Naumkin and Wales. In contrast to the DIM method, the HPP formalism predicts the excitation to localise mostly on two atoms rather than three, for the relaxed geometry of the lowest triplet state. The hole localisation on a dimer is associated to the appearance of a large electric dipole, which depends on the isomer geometry. This dipole indicates the strong Pauli repulsion experienced by the Rydberg electron, which pushes it out of the cluster. For clusters at their ground state equilibrium geometry, we observe the formation of a singlet-state band associated with the Ar orbital, well separated from the upper states, which matches quite well with the so-called surface exciton band observed experimentally.

Do not forget the Rydberg orbitals.

Within any molecule or cluster containing one or more positively charged sites, families of Rydberg orbitals exist. Free electrons can attach directly, and anionic reagents with low electron binding energy can transfer an electron into one of these orbitals to form a neutral Rydberg radical. The possibilities that such a radical could form a covalent bond either to another Rydberg radical or to a radical holding its electron in a conventional valence orbital are considered. This Perspective overviews two roles that Rydberg radicals can play, both of which have important chemical consequences. Attachment of an electron into excited Rydberg orbitals is followed by rapid (∼10-6s) relaxation into the lowest-energy Rydberg orbital to form the ground state radical. Although the excited Rydberg species are stable with respect to fragmentation, the ground-state species is usually quite fragile and undergoes homolytic bond cleavage (e.g., -R2NH dissociates into -R2N + H or into -RNH + R) by overcoming a very small barrier on its potential energy surface, thus generating reactive radicals (H or R). Here, it is shown that as a result of this fragility, any covalent bonds formed by Rydberg radicals are weak and the molecules they form are susceptible to exothermic fragmentations that involve quite small activation barriers. Another role played by Rydberg species arises when the Coulomb potentials provided by the (one or more) positive site(s) in the molecule stabilize low-energy anti-bonding orbitals (e.g., σ* orbitals of weak σ bonds or low-lying π* orbitals) to the extent that electron attachment into these Coulomb-stabilized orbitals is rendered exothermic. In such cases, the overlap of the Rydberg orbitals on the positive site(s) with the σ* or π* orbitals allows either a free electron or a weakly bound electron to an anionic reagent that is attracted toward the positive site by its Coulomb force to be guided/transferred into the σ* or π* orbital instead. After attaching to such an anti-bonding orbital, bond cleavage occurs again, generating reactive radical species. Because of the large radial extent of Rydberg orbitals, this class of bond cleavage events can occur quite distant from the positively charged group. In this Perspective, several examples of both types of phenomena are given for illustrative purposes.

Electronic structure of the ground and excited states of neutral and charged silicon hydrides, SiHx0/+/−, x = 1–4

The ground and excited electronic states of the titled species are investigated with multi-reference configuration interaction and diffuse basis sets. We found that in addition to the valence orbitals, the inclusion of the 4s, 4p, and especially 3d orbitals (although with minimal population) of silicon in the active space of the reference complete active space self-consistent field wavefunction are necessary for the proper convergence of the calculations. We also demonstrate that the aug-cc-pVTZ basis set provides quite accurate results compared to both larger basis sets and basis set limit results at a lower computational cost. The excited states involve excitations within the 3s and 3p orbitals of silicon (especially for the mono- and di-hydrides), followed by excitations from the Si-H bonding orbitals to either silicon valence or Rydberg (4s, 4p) orbitals. The number of electronic states per energy unit decrease as we add hydrogen atoms, and the first excited state of SiH4 is at 9.0 eV and leads to SiH3 + H. All species have stable ground state structures with all hydrogen atoms bound to silicon, except for SiH4+ and SiH4-. The former dissociates to SiH2+ + H2, while the latter loses an electron or can dissociate forming H2 as well.

Superatomic Rydberg State Excitation.

Superatomic molecular orbitals (SAMOs) have symmetries (angular quantum numbers) similar to those of atoms, and thus, it is possible to realize Rydberg state excitations (RSEs) in superatomic molecules. In this Letter, the feasibility of superatomic Rydberg state excitation (SRSE) is explored using gold superatoms based on first-principles calculations. The results show that the SRSE exists in the high and low excited states of the gold superatoms and their SAMOs make a major contribution to electronic transitions. The radial distribution function of electronic density shows that the main distribution of electrons in the lowest unoccupied molecular orbitals and other unoccupied superatomic molecular orbitals is extremely far from the geometric center, and thus, they can be unambiguously identified as Rydberg orbitals. We found that due to the two-dimensional ductility of the planar SAMOs, superatoms are superior in the RSE regulation. Our findings may provide a new source of superatom-based RSE and will contribute to the regulation and efficient preparation of Rydberg states.

Electronic Structure of Liquid Alkanes: A Representative Case of Liquid Hexanes and Cyclohexane Studied Using Polarization-Dependent Two-Photon Absorption Spectroscopy.

Two-photon absorption (2PA) spectra of liquid cyclohexane and hexanes are reported for the energy range 6.4-8.5 eV (177-145 nm), providing detailed information about their electronic structures in bulk liquid. Using a broadband pump-probe fashion, we measured the continuous 2PA spectra by simultaneous absorption of a 266 nm (4.6 eV) pump photon and one UV-vis probe photon from the white-light continuum (1.8-3.9 eV). Theoretical one-photon absorption (1PA) and 2PA cross sections of isolated gas phase molecules are computed by the equation of motion coupled-cluster method with single and double substitutions (EOM-CCSD) to substantiate the assignment of the experimental spectra, and the natural transition orbital (NTO) analysis provides visualization of the participating orbitals in a transition. Our analysis suggests that upon solvation transitions at the lowest excitation energy involving promotion of electron to the 3s Rydberg orbitals are blue-shifted (∼0.55 eV for cyclohexane and ∼0.18 eV for hexanes) to a greater extent as compared to those involving other Rydberg orbitals, which is similar to the behavior observed for water and alcohols. All other transitions experience negligible (cyclohexane) or minor red-shift by ∼0.15-0.2 eV (hexane) upon solvation. In both alkanes, the spectra are entirely dominated by Rydberg transitions: the most intense bands in 1PA and 2PA spectra are due to the excitation of electrons to the Rydberg "p" and "d" type orbitals, respectively, although one transition terminating in the 3s Rydberg has significant 2PA strength. This work demonstrates that the gas phase electronic transition properties in alkanes are not significantly altered upon solvation. In addition, electronic structure calculations using an isolated-molecule framework appear to provide a reasonable starting point for a semiquantitative picture for spectral assignment and also to analyze the solvatochromic shifts for liquid phase absorption spectra.

Electron attachment to representative cations composing ionic liquids.

Using ab initio electronic structure methods with flexible atomic orbital basis sets, we investigated the electronic structure and stability of reduction products of selected representative cations (C+) constituting ionic liquids. We found that an electron attachment to such cations leads to the neutral radicals, whereas a subsequent attachment of another (i.e., excess) electron leads to adiabatically stable anions only in two cases {[P(CH3)4]- and [MeMePyr]-}. The possibility of the formation of various dimers (such as CC+, CC, and CC-) was also considered, and the resulting systems were characterized by predicting their lowest energy structures, ionization potentials, electron affinities, and susceptibilities to the fragmentation process. Among the cations studied, only the [MeMePyr]+ was found to form a typical Rydberg radical (MeMePyr) and double-Rydberg anion ([MeMePyr]-), whereas the remaining cations were predicted to form neutral radicals of a primarily valence (MeMeIm and MePy) or mixed Rydberg-valence [P(CH3)4] character. Our calculations confirmed the stability of all CC+ and CC dimers against fragmentation yielding the corresponding monomers (the binding energies of 12.2-20.5 kcal/mol and 11.3-72.3 kcal/mol were estimated for CC+ and CC dimers, respectively). [(MeMePyr)2]- was identified as the only adiabatically stable CC- dimeric anion having its vertical electron detachment energy of 0.417 eV. We also found that in the [(MeMePyr)2]- anionic state, three outermost electrons are described by Rydberg orbitals, which results in the (σ)2(σ*)1 configuration.

Superatomic Rydberg State Excitation

Superatomic molecular orbitals (SAMOs) have symmetries (angular quantum numbers) similar to those of atoms and thus it is possible to realize Rydberg state excitations (RSEs) in superatomic molecules. In this letter, the feasibility of superatomic Rydberg state excitation (SRSE) is explored using gold superatoms based on first-principles calculations. The results show that the SRSE exists in both the high and low excited states of the gold superatoms and their SAMOs make a major contribution to electronic transitions. The radial distribution function (RDF) of electronic density shows that the main distribution of electrons in the lowest unoccupied molecular orbitals and other unoccupied superatomic molecular orbitals is extremely far from the geometric center and thus they can be unambiguously identified as Rydberg orbitals. We found that due to two-dimensional ductility of planar superatoms’ transition orbitals, superatoms have the superiority in RSE regulation. Our findings provide a new source of superatom-based RSE and will contribute to the regulation and efficient preparation of Rydberg states.

Difference in the electron energy loss spectra between the spinel-type Na3LiTi5O12 and Li4Ti5O12 clarified by density functional theory calculations

Li4Ti5O12 is an anode material for Li-ion batteries, and Na3LiTi5O12 is a candidate anode material for Na-ion batteries. Both materials have a spinel framework of Ti–O bonds; hence, the electronic structures are similar. However, the difference between Li4Ti5O12 and Na3LiTi5O12 is detected via electron energy loss spectra (EELS). Density functional theory calculations of the highest energy regions of the titanates show that the difference is caused by the orbital overlaps between the Rydberg orbitals of the O atoms in the 32e sites and alkali metal atoms in the 8a sites. When the 8a sites are occupied by Li, the interaction becomes large, and the peaks in the density of states and EELS become sharp. In contrast, when the 8a sites are occupied by Na, the interaction becomes small, and the peaks in the density of states and EELS become broad. These results imply that the cations in the 8a sites can interact with the Ti–O spinel framework and affect the resulting properties.

N-derivatives of formaldimines: the reason for the high nitrogen inversion barriers in N-methyl- and N-chloroimines

The energy and electronic parameters of the nitrogen inversion in imines Н 2 С=NХН n (ХН n = СН 3 , NH 2 , OH, F, SiH 3 , PH 2 , SH, Cl) have been calculated with the DFT method (B3LYP 6-311+G(d,p)) in terms of natural bond orbital. It has been established that the interactions of the nitrogen lone pair (LP) with the bond orbitals at the imino carbon atom are practically independent of the X atom and contribute to the decrease of the inversion barriers (Δ Е і ≠ ). While nN®σ * X–H , nN«σ X–H and nN«nX interactions substantially depend on the heteroatom type and promote the increase in the Δ Е і ≠ values with the rise in electronegativity of the X atom. The contribution of the interactions of the nitrogen LP with the Rydberg orbitals of the C=N–X group atoms is small and they cannot be the main reason of the decrease in the Δ Е і ≠ values when X atoms of the second period are replaced by atoms of the third period of the same group. The interactions of the LP of the X atoms and the X–H bond orbitals with the C=N bond orbitals have the main influence on the inversion barriers. The contribution of nX®π * C=N interactions to the Δ Е і ≠ values is dominant. The main reason of the “anomalous” inversion barriers of N-methyl- and N-chloroformaldimines is the destabilization of inversion transition states because of the reduction in the energies of σ X–H ®π * C=N and nX→π * C=N interactions and the rise in the energies of nN«nСl interactions. The contributions of electronegativity of ХН n substituents and energies of intramolecular interactions to the Δ Е і ≠ values have been determined.