Cationic States Research Articles

Vibronic Coupling Effects in the Photoelectron Spectrum of Ozone: A Coupled-Cluster Approach.

One of the most important areas of application for equation-of-motion coupled-cluster (EOM-CC) theory is the prediction, simulation, and analysis of various types of electronic spectra. In this work, the EOM-CC method for ionized states, known as EOM-IP-CC, is applied to the closely lying and coupled pair of states of the ozone cation─X̃2A1 and Ã2B2─using highly accurate treatments including up to the full single, double, triple, and quadruple excitations (EOM-IP-CCSDTQ). Combined with a venerable and powerful method for calculating vibronic spectra from the Hamiltonian produced by EOM-IP-CC calculations, the simulations yield a spectrum that is in good agreement with the photoelectron spectrum of ozone. Importantly, the calculations suggest that the adiabatic gap separating these two electronic states is somewhat smaller than currently thought; an assignment of the simulated spectrum together with more precise band positions of the experimental measurements suggests T00 = 1,368 ± 65 cm-1.

Electric‐Field Catalysis on Carbon Nanotubes in Electromicrofluidic Reactors: Monoterpene Cyclizations

AbstractThe control over the movement of electrons during chemical reactions with oriented external electric fields (OEEFs) has been predicted to offer a general approach to catalysis. Recently, we suggested that many problems to realize electric‐field catalysis in practice under scalable bulk conditions could possibly be solved on multiwalled carbon nanotubes in electromicrofluidic reactors. Here, we selected monoterpene cyclizations to assess the scope of our system in organic synthesis. We report that electric‐field catalysis can function by stabilizing both anionic and cationic transition states, depending on the orientation of the applied field. Moreover, electric‐field catalysis can promote reactions which are barely accessible by general Brønsted and Lewis acids and field‐free anion‐π and cation‐π interactions, and drive chemoselectivity toward intrinsically disfavored products without the need for pyrene interfacers attached to the substrate to prolong binding to the carbon nanotubes. Finally, interfacing with chiral organocatalysts is explored and evidence against contributions from redox chemistry is provided.

Impact of chlorine substitution on valence orbitals and ionization dynamics in 3-chloropyridine: Insights from high-resolution vacuum ultraviolet mass-analyzed threshold ionization study.

In this study, the effects of chlorine substitution on the valence orbitals and electronic states of 3-chloropyridine (3-CP) were investigated utilizing high-resolution vacuum ultraviolet mass-analyzed threshold ionization (VUV-MATI) spectroscopy and computational methods. High-quality vibrational spectra were obtained from the VUV-MATI spectra of 3-CP isotopomers (35Cl and 37Cl), revealing high-quality vibrational spectra for the lowest cationic states. The adiabatic ionization energies (AIEs) of these isotopomers were accurately determined, providing detailed information about the electronic structure and ionization dynamics. Intense spectra peaks were linked with the D1 excited state of the 3-CP cation, with vibronic transitions in this state closely matching those predicted by Franck-Condon simulations. This provided insights into the cationic structure and the roles of the highest occupied molecular orbital (HOMO) and the HOMO-1. The HOMO was primarily a π orbital of the pyridine ring, while the HOMO-1 consisted of nonbonding orbitals. The AIEs suggested that meta-chlorine substitution stabilizes nonbonding orbitals less effectively than ortho substitution, indicating closely spaced electronic states in the 3-CP cation. Minor discrepancies in vibrational frequencies and intensities, particularly above 800cm-1, suggested the presence of vibronic coupling, warranting further investigation. Overall, this study provided a comprehensive understanding of the vibronic and ionization properties of 3-CP, emphasizing the influence of the position of the chlorine substitution on molecular orbitals and the value of advanced theoretical and experimental approaches for analyzing the vibrational spectra of complex molecules.

Vibrational assignments and energy analyses of 3,4-difluorophenylacetylene using resonance-enhanced multiphoton ionization and slow electron velocity-map imaging techniques

Here, we report spectroscopic investigations of 3,4-difluorophenylacetylene applying two-color resonant two-photon ionization (2C-R2PI) and slow electron velocity-map imaging (SEVI) techniques. With the assistance of density functional theory (DFT) calculations, vibrational modes of the S0 neutral ground state, S1 first electronic excited state, and D0 cationic ground state were assigned. The adiabatic excitation energy of the S1 ← S0 electronic transition was determined to be 35639 ± 5 cm−1 from the resonance-enhanced multiphoton ionization (REMPI) spectroscopy. Additionally, the adiabatic ionization potential was found to be 72398 ± 5 cm−1 based on the SEVI spectra.

Nitrogen‐Nitrogen Bond Breaking in Irradiation Products of Hexanitrohexaazaisowurtzitane (CL‐20)

AbstractWhile the primary result of an interaction of ionizing radiation with an organic material is the ejection of electrons from molecular orbitals producing cations, the free electrons can further interact, yielding excited states; and, potentially, anions. In this work, we computed reaction barriers and energies for N−N bond breaking in the CL‐20 cation, anion, and excited state to investigate if CL‐20 degradation is accelerated after radiation exposure. We focused on N−N bond dissociation because it is the rate‐determining step in the thermal degradation of CL‐20. We found that N−N cleavage rapidly takes place in the CL‐20 cation and anion with greatly reduced reaction energies as compared to CL‐20. We also outlined a potential path for photodissociation of the N−N bond. While CL‐20 is kinetically stable, initial degradation occurs readily in its irradiation products. This is of importance for the performance of the explosive after high‐dose exposure and influences aging if CL‐20 is irradiated at a low dose over extended periods of time.

Molecular Association and Reactivity of the Pyridine Dimer Cation.

A recent experimental report has identified the formation of the C-N hemibonded pyridine dimer cation following vacuum ultraviolet near-threshold photoionization [J. Phys. Chem. Lett., 2021, 12, 4936-4943]. Herein, the dynamics and consequent reactivity of the pyridine dimer cation were investigated employing Born-Oppenheimer molecular dynamics (BOMD) simulations. An antiparallel π-stacked pyridine dimer in the neutral ground state is transformed into a noncovalently interacting C-H···N hydrogen-bonded structure which can lead to proton transfer in the cationic state. Additionally, C-N- and N-N-bonded adducts were formed in the cationic state. Further, metastable C-H···H-C-bonded cationic species was observed, which rearranged to an N-N bonded adduct. In contrast to the experimental observation, migration of the proton to the α position was not observed in the C-N bonded adduct owing to a high barrier of about 2 eV. The observed trends in the molecular association, proton transfer, and the formation of C-N and N-N bonded adducts are a consequence of the roaming dynamics of one pyridine moiety over the other in the cationic state.

Spiro-Buckybowls: Synthesis and Selective Transformations Toward Chiral and Nonlinear Optical Polycycles.

Integration of spirocycles with buckybowls is a promising strategy to construct three-dimensional (3D) curved π-systems and to endow distinctive physicochemical features arising from buckybowls. Herein, a series of carbon-bridged spiro-type heterosumanenes (spiro-HSEs) were synthesized by combining 9,9'-spirobifluorene and dichalcogenasumanenes (DCSs). It is found that spiro-conjugation plays an important role in the geometric and electronic structures of spiro-HSEs. The bowl depth of DCSs moiety becomes larger in the spiro-HSEs. Owing to the Jahn-Teller (J-T) effect, two DCSs segments of spiro-HSEs have different bowl depths accompanied with the unequal distribution of charge in radical cation state. Taking advantage of the typical reactions of DCSs, selective transformations of spiro-HSEs have been adopted in accordance to the nature of chalcogen atoms (S, Se, Te) to bestow the value-added functionalities. The emissive property is enhanced by converting the thiophene rings of S-doped spiro-HSE into thiophene S,S-dioxides. A chiroptical polycycle could be produced by ring-opening of the edge benzene of Se-doped spiro-HSE. The covalent adduct of Te-doped spiro-HSE with Br2 forms non-centrosymmetric halogen-bonded networks, resulting in the high performance second-order nonlinear optics (NLO).

Spiro‐Buckybowls: Synthesis and Selective Transformations Toward Chiral and Nonlinear Optical Polycycles

AbstractIntegration of spirocycles with buckybowls is a promising strategy to construct three‐dimensional (3D) curved π‐systems and to endow distinctive physicochemical features arising from buckybowls. Herein, a series of carbon‐bridged spiro‐type heterosumanenes (spiro‐HSEs) were synthesized by combining 9,9′‐spirobifluorene and dichalcogenasumanenes (DCSs). It is found that spiro‐conjugation plays an important role in the geometric and electronic structures of spiro‐HSEs. The bowl depth of DCSs moiety becomes larger in the spiro‐HSEs. Owing to the Jahn‐Teller (J‐T) effect, two DCSs segments of spiro‐HSEs have different bowl depths accompanied with the unequal distribution of charge in radical cation state. Taking advantage of the typical reactions of DCSs, selective transformations of spiro‐HSEs have been adopted in accordance to the nature of chalcogen atoms (S, Se, Te) to bestow the value‐added functionalities. The emissive property is enhanced by converting the thiophene rings of S‐doped spiro‐HSE into thiophene S,S‐dioxides. A chiroptical polycycle could be produced by ring‐opening of the edge benzene of Se‐doped spiro‐HSE. The covalent adduct of Te‐doped spiro‐HSE with Br2 forms non‐centrosymmetric halogen‐bonded networks, resulting in the high performance second‐order nonlinear optics (NLO).

Electrical monitoring of single-event protonation dynamics at the solid-liquid interface and its regulation by external mechanical forces

Detecting chemical reaction dynamics at solid-liquid interfaces is important for understanding heterogeneous reactions. However, there is a lack of exploration of interface reaction dynamics from the single-molecule perspective, which can reveal the intrinsic reaction mechanism underlying ensemble experiments. Here, single-event protonation reaction dynamics at a solid-liquid interface are studied in-situ using single-molecule junctions. Molecules with amino terminal groups are used to construct single-molecule junctions. An interfacial cationic state present after protonation is discovered. Real-time electrical measurements are used to monitor the reversible reaction between protonated and deprotonated states, thereby revealing the interfacial reaction mechanism through dynamic analysis. The protonation reaction rate constant has a linear positive correlation with proton concentration, whereas the deprotonation reaction rate constant has a linear negative correlation. In addition, external mechanical forces can effectively regulate the protonation reaction process. This work provides a single-molecule perspective for exploring interface science, which will contribute to the development of heterogeneous catalysis and electrochemistry.

Electric-Field Catalysis on Carbon Nanotubes in Electromicrofluidic Reactors: Monoterpene Cyclizations.

The control over the movement of electrons during chemical reactions with oriented external electric fields (OEEFs) has been predicted to offer a general approach to catalysis. Recently, we suggested that many problems to realize electric-field catalysis in practice under scalable bulk conditions could possibly be solved on multiwalled carbon nanotubes in electromicrofluidic reactors. Here, we selected monoterpene cyclizations to assess the scope of our system in organic synthesis. We report that electric-field catalysis can function by stabilizing both anionic and cationic transition states, depending on the orientation of the applied field. Moreover, electric-field catalysis can promote reactions which are barely accessible by general Brønsted and Lewis acids and field-free anion-π and cation-π interactions, and drive chemoselectivity toward intrinsically disfavored products without the need for pyrene interfacers attached to the substrate to prolong binding to the carbon nanotubes. Finally, interfacing with chiral organocatalysts is explored and evidence against contributions from redox chemistry is provided.

Laser Spectroscopic Characterization of Supersonic Jet-Cooled 2,6-Diazaindole (26DAI).

The article presents a comprehensive laser spectroscopic characterization of a nitrogen-rich indole derivative, namely, 2,6-diazaindole (26DAI), in the gas phase. A supersonic jet-cooled molecular beam of 26DAI was characterized using two-color resonant two-photon ionization (2C-R2PI) and laser-induced fluorescence spectroscopy (LIF) to investigate the electronic excitation. The S1 ← S0 origin transition was obtained at 33915 cm-1, which was red-shifted from that of one (indole) and two (7-azaindole) nitrogen-containing indole derivatives by 1317 and 713 cm-1, respectively. The molecular orbital and energy analysis for the S1 ← S0 transition shows the significant stabilization of LUMO on subsequent N-insertion, resulting in the lowering of the S1 ← S0 (ππ*) transition energy. The single vibronic level fluorescence spectrum from the vibrationless S1 state of the molecule was recorded. The spectrum displayed an extensive Franck-Condon activity until 2500 cm-1 for the vibrational modes of the S0 state of the 26DAI molecule. The experimental ground state vibrational frequencies were compared to the calculated ones obtained at three different levels of theories. More accurate results were found at DFT B3LYP-D4 than those at the wave function-based MP2 and CCSD levels of theories. Further, the N-H stretching frequency of 26DAI in the S0 state was measured at 3524 cm-1 using fluorescence-dip infrared (FDIR) spectroscopy. The stability of 26DAI against ionization radiation was probed by measuring the two-color photoionization energy (IE2P) of 26DAI at 71866 cm-1. The IE2P value is significantly higher than those of N-poor counterparts (indole and 7-azaindole). The NBO charges and spin density (SD) values of the 26DAI molecule have shown that electronegative N(6) makes the cationic ground state less stable due to the position of the positive centers on the N atom. The results provided insights into the stability of N-rich biomolecules against photodamage. The current investigation can shed light on nature's way of stabilizing biomolecules with a possible N-insertion mechanism.

Vibronic coupling in the energetically six lowest electronic states of oxirane radical cation.

Multi-dimensional quantum mechanical simulations are carried out to understand the multi-state and multi-mode vibronic interactions in the first six low-lying viz., X̃2B1, Ã2A1, B̃2B2, C̃2A2, D̃2A1, and Ẽ2B1 electronic states of c-C2H4O·+. Vibronic coupling theory is applied to study interactions among electronic states using symmetry selection rules. A model 6 × 6 diabatic electronic Hamiltonian is constructed. The parameters of the diabatic Hamiltonian are estimated by performing extensive abinitio electronic structure calculations, using the EOM-IP-CCSD method. The nuclear dynamics calculations are performed with both time-independent and time-dependent quantum mechanical methods. The calculated vibronic structures of six electronic states are found to be in excellent agreement with the available experimental findings. Progressions found in the theoretical spectrum are assigned in terms of vibrational modes. It is found that extremely strong vibronic interactions among the X̃2B1-Ã2A1, B̃2B2-C̃2A2, and D̃2A1-Ẽ2B1 electronic states results into highly overlapping vibronic bands due to multiple multi-state conical intersections. The impact of associated nonadiabatic effects on the vibronic structure and dynamics of the mentioned electronic states is examined at length. Interesting comparison is made with the results obtained for the isomeric acetaldehyde radical cation.

Highly Acidic Electron-Rich Brønsted Acids Accelerate Asymmetric Pictet-Spengler Reactions by Virtue of Stabilizing Cation-π Interactions.

Electron-rich heteroaromatic imidodiphosphorimidates (IDPis) catalyze the asymmetric Pictet-Spengler reaction of N-carbamoyl-β-arylethylamines with high stereochemical precision. This particular class of catalysts furthermore provides a vital rate enhancement compared to related Brønsted acids. Here we present experimental studies on the underlying reaction kinetics that shed light on the specific origins of rate acceleration. Analysis of Hammett plots, kinetic isotope effects, reaction orders, Eyring plots, and isotopic scrambling experiments, allowed us to gather insights into the molecular interactions between the chiral Brønsted acid and catalytically formed intermediates. Based on rigorously determined pKa values as well as the experimental evidence, we propose that attractive intermolecular forces offered by electron-rich π-surfaces of the chiral counteranion enthalpically stabilize cationic intermediates and transition states by way of cation-π interactions. This view is furthermore supported by in-depth density functional theory calculations. Our deepened understanding of the reaction mechanism allowed us to develop a method for accessing 1-aryltetrahydroisoquinolines from aromatic dimethyl acetals, a substrate class that was thus far inaccessible via catalytic asymmetric Pictet-Spengler reactions.

Few-femtosecond electron transfer dynamics in photoionized donor-π-acceptor molecules.

The exposure of molecules to attosecond extreme-ultraviolet (XUV) pulses offers a unique opportunity to study the early stages of coupled electron-nuclear dynamics in which the role played by the different degrees of freedom is beyond standard chemical intuition. We investigate, both experimentally and theoretically, the first steps of charge-transfer processes initiated by prompt ionization in prototype donor-π-acceptor molecules, namely nitroanilines. Time-resolved measurement of this process is performed by combining attosecond XUV-pump/few-femtosecond infrared-probe spectroscopy with advanced many-body quantum chemistry calculations. We show that a concerted nuclear and electronic motion drives electron transfer from the donor group on a sub-10-fs timescale. This is followed by a sub-30-fs relaxation process due to the probing of the continuously spreading nuclear wave packet in the excited electronic states of the molecular cation. These findings shed light on the role played by electron-nuclear coupling in donor-π-acceptor systems in response to photoionization.

Strong Electron-Electron-Nuclei Correlations in Two-Photon Double Ionization of H_{2}.

Two-photon double ionization is a paradigmatic example of how electron correlation manifests. In molecular targets, its coupling with the slower nuclear motion introduces an additional complication and induces electron-electron-nuclei correlations. Experimentally, momentum-coincident measurements can provide a complete kinematical image of the molecular full Coulomb breakup. Previous theoretical studies have described this process by ignoring nuclear motion and the subsequent Coulomb explosion of the dication. Here we show, by means of a full-dimensional treatment of two-photon double ionization of the H_{2} molecule, that nuclear motion plays a decisive role even for pulses as short as 1.5fs, a time during which the nuclei are not expected to move significantly. We find strong correlations between nuclear and electronic degrees of freedom, giving access to different electronic processes as a function of nuclear kinetic energy. In particular, we observe unexpectedly strong back-to-back asymmetry in the photoelectron angular distributions, as well as novel interferences resulting from the coherent contributions from two-photon sequential absorption paths via different molecular cationic states.

Mix and Match Tuning of the Conformational and Multistate Redox Switching Properties of an Overcrowded Alkene.

Overcrowded alkenes have received considerable attention as versatile structural motifs in a range of optical switches and light-driven unidirectional motors. In contrast, their actuation by electrochemical stimuli remains underexplored, even though this alternative energy input may be preferred in various applications and enables additional control over molecular switching states and properties. While symmetric bistricyclic overcrowded enes (BAEs) containing two identical halves based on either thioxanthene (TX) or acridine (Acr) motifs are known to be reversible conformational redox switches, their redox potentials are generally too high or low, respectively, thereby preventing wider applications. Herein, we demonstrate that the "mixed" TX-Acr switch possesses redox properties that lie between those of its parent symmetric analogs, enabling interconversion between three stable redox and conformational states at mild potentials. This includes the neutral anti-folded, the dicationic orthogonal, and a unique twisted monoradical cation state, the latter of which is only accessible in the case of the mixed TX-Acr switch and in a pathway-dependent manner. Consequently, with this multistate redox switch, a myriad of molecular properties, including geometry, polarity, absorbance, and fluorescence, can be modulated with high fidelity and reversibility between three distinct stable states. More generally, this study highlights the versatility of the "mix and match" approach in rationally designing redox switches with specific (redox) properties, which in turn is expected to enable a myriad of applications ranging from molecular logic and memory to actuators and energy storage systems.

Investigation of Key Electronic States in Layered Mixed Chalcogenides With a d0 Transition Metal as Li‐Ion Cathodes

AbstractLithium‐rich transition metal chalcogenides are witnessing a revival as candidates for Li‐ion cathode materials, spurred by the boost in their capacities from transcending conventional redox processes based on cationic states and tapping into additional chalcogenide states. A particularly striking case is Li2TiS3‐ySey, which features a d0 metal. While the end members are expectedly inactive, substantial capacities are measured when both Se and S are present. Using X‐ray absorption spectroscopy, it is shown that the electronic structure of Li2TiS3‐ySey is not a simple combination of the end members. The data confirm previous hypotheses that, in Li2TiS2.4Se0.6, this behavior is underpinned by concurrent and reversible redox of only S and Se, and identify key electronic states. Moreover, wavelet transforms of the extended X‐ray absorption fine structure provide direct evidence of the formation of short Se–Se units upon charging. The study uncovers the underpinnings of this intriguing reactivity and highlights the richness of redox chemistry in complex solids.

Valence Electronic Structure of Interfacial Phenol in Water Droplets.

Biochemistry and a large part of atmospheric chemistry occur in aqueous environments or at aqueous interfaces, where (photo)chemical reaction rates can be increased by up to several orders of magnitude. The key to understanding the chemistry and photoresponse of molecules in and "on" water lies in their valence electronic structure, with a sensitive probe being photoelectron spectroscopy. This work reports velocity-map photoelectron imaging of submicrometer-sized aqueous phenol droplets in the valence region after nonresonant (288 nm) and resonance-enhanced (274 nm) two-photon ionization with femtosecond ultraviolet light, complementing previous liquid microjet studies. For nonresonant photoionization, our concentration-dependent study reveals a systematic decrease in the vertical binding energy (VBE) of aqueous phenol from 8.0 ± 0.1 eV at low concentration (0.01 M) to 7.6 ± 0.1 eV at high concentration (0.8 M). We attribute this shift to a systematic lowering of the energy of the lowest cationic state with increasing concentration caused by the phenol dimer and aggregate formation at the droplet surface. Contrary to nonresonant photoionization, no significant concentration dependence of the VBE was observed for resonance-enhanced photoionization. We explain the concentration-independent VBE of ∼8.1 eV observed upon resonant ionization by ultrafast intermediate state relaxation and changes in the accessible Franck-Condon region as a consequence of the lowering of the intermediate state potential energy due to the formation of phenol excimers and excited phenol aggregates. Correcting for the influence of electron transport scattering in the droplets reduced the measured VBEs by 0.1-0.2 eV.

UV wavelength-dependent photoionization quantum yields for the dark 1nπ* state of aqueous thymidine.

Despite the important role of the dark 1nπ* state in the photostability of thymidine in aqueous solution, no detailed ultraviolet (UV) wavelength-dependent investigation of the 1nπ* quantum yield (QY) in aqueous thymidine has been experimentally performed. Here, we investigate the wavelength-dependent photoemission spectra of aqueous thymidine from 266.7 to 240 nm using liquid-microjet photoelectron spectroscopy. Two observed ionization channels are assigned to resonant ionizations from 1ππ* to the cationic ground state D0 (π-1) and 1nπ* to the cationic excited state D1 (n-1). The weak 1nπ* → D1 ionization channel appears due to ultrafast 1ππ* → 1nπ* internal conversion within the pulse duration of ∼180 fs. The obtained 1nπ* quantum yields exhibit a strong wavelength dependence, ranging from 0 to 0.27 ± 0.01, suggesting a hitherto uncharacterized 1nπ* feature. The corresponding vertical ionization energies (VIEs) of D0 and D1 of aqueous thymidine are experimentally determined to be 8.47 ± 0.12 eV and 9.22 ± 0.29 eV, respectively. Our UV wavelength-dependent QYs might indicate that different structural critical points to connect the multidimensional 1ππ*/1nπ* conical intersection seam onto the multidimensional potential energy surface of the 1ππ* state might exist and determine the relaxation processes of aqueous thymidine upon UV excitation.

Photoionization of aziridine: Nonadiabatic dynamics of the first six low-lying electronic states of the aziridine radical cation.

In this article, the theoretical photoionization spectroscopy of the aziridine (C2H5N) molecule is investigated. To start with, we have optimized the geometry of this molecule at the neutral electronic ground state at the density functional theory/augmented correlation-consistent polarized valence triple zeta level of theory using the G09 program. The electronic structure calculations were restricted to the first six low-lying electronic states in order to account for the experimental photoelectron spectrum of the C2H5N molecule. The first six low-lying electronic states (X̃2A', Ã2A', B̃2A″, C̃2A″, D̃2A', and Ẽ2A') of the potential energy surfaces (PESs) are calculated by both equation of motion-ionization potential-coupled cluster singles and doubles and multi-configuration quasi-degenerate perturbation theory abinitio quantum chemistry methods along the dimensionless normal displacement coordinates in which multiple conical intersections were established among the considered electronic states. A (6 × 6) model vibronic Hamiltonian is constructed on a diabatic electronic basis, using the symmetry selection rules and Taylor series expansion. The Cs symmetry point group of the aziridine molecule leads to electronic states symmetry of either A' or A″, and these states are close in energy, due to which the same symmetry electronic states avoid each other. To get a smooth diabatic PES, a fourfold diabatization scheme is used, which is implemented in the General Atomic and Molecular Electronic Structure Systems suite of programs. All the parameters used in the diabatic vibronic coupling model Hamiltonian are calculated in terms of the normal modes of vibrational coordinates. Finally, the vibronic model Hamiltonian constructed for the coupled six electronic states is used to solve both time-independent and time-dependent Schrödinger equations using the multi-configuration time-dependent Hartree program module to obtain the dynamical observables. The theoretical vibronic band structure is found to be in good accord with the available experimental results.