Theoretical study of single-electron capture in He2+ —H− collision

We present a detailed theoretical treatment of single-electron transfer between He²⁺ and H^?. The total cross section is calculated using stationary molecular states which are appropriate in the energy range covered by the experiments (between 0.5 and 2250 eV in the centre of mass frame). We use an expansion on a two-electron basis built with one-electron diatomic molecule (OEDM) orbitals and including the common translation factor of Errea et al. All coupling terms are calculated explicitly. Because of the small binding energy of H^? compared to that of the ground state of He⁺, capture occurs into highly excited states of He⁺. Results obtained with a straight-line quasiclassical calculation are in good agreement with the experimental data. At low energy, He⁺ (n=5) +H(1s) is the dominant capture channel; at higher energy, the He⁺ (n=4) + H(1s) channel becomes important. The rise in the cross section below 6 eV can be attributed to the Coulomb attraction in the incoming channel. To account for this effect, a fully quantal calculation has been performed. The agreement with the low-energy measurements is then excellent.     

Isotopically resolved {ie30-01} electronic spectrum of Ag3 and calculation of its Jahn-Teller effects

Ag₃ was produced by pulsed-nozzle laser vaporisation and jet-cooled in a Ne supersonic expansion. Onecolor resonant two-photon ionisation (R2PI) spectra of the {ie30-02} transition of Ag₃ were separately measured for all four isotopic combinations. Long vibrational progressions are observed, involving clearly resolved bands at low energy, merging into a dense but resolvable spectrum up to 1000 cm¹ above the origin. Both the ground {ie30-03} and excited {ie30-04} states of Ag3 are susceptible to Jahn-Teller distortion along the degenerate e′ bending coordinate. The Jahn-Teller analysis includes both linear and quadratic terms, simultaneously with the spin-orbit coupling. Following extensive parameter fitting, the absorption spectrum is calculated, and bands assigned. The spin-orbit splitting is quenched below the localization energy, but becomes observable ≈ 300 cm^-1 above the origin.     

A short CI expansion for a symmetry-adapted description of localized hole states: Application to the 3dσu hole state of the Cu2 + ion

A simple formalism is developed to describe by means of a symmetry-adapted wavefunction the localized hole states which may arise in symmetric systems. A short CI expansion is generated in a systematic way from the delocalized molecular orbitals of the SCF ground state. For the 3dσ_u hole state of the _Cu2 ⁺ ion, the symmetry adapted and the broken symmetry solutions approximately correspond to the same energy at that level of CI.     

Near threshold channel selective photodissociation of NO2

The dynamics of the photodissociation of NO₂ into NO(X ²Π_Ω″, ν″=0,J″)+O(³ P _0,1,2) is investigated near the thermodynamic threshold. Cooling the internal degrees of freedom by a supersonic beam expansion provides a nearly complete quantum state selection prior to the predissociation. Measurements of the wavelength dependent dissociation yield into specific product quantum states are reported. At certain wavelengths Λ″ doublet resolved rotational population distributions of the fragments are obtained. Up to an excess energy ofE _exc=121 cm^?1 about 42% of this energy is partitioned into the rotation of the NO molecules, and correspondingly 58% into the translational degree of freedom. The role of electronic and total parity is discussed.     

Analysis of approximations and errors in equations of motion method calculations

We analyze a number of fundamental questions associated with the use of a finite one-particle orbital basis in equations of motion (EOM) method calculations of excitation energies etc., of atomic and molecular systems. This approximation yields an approximate n_e-electron ground state and say, N excited states, while there are (N + 1)² different possible basis operators for EOM calculations. We show that sets of at most 2N basis operators can contribute to the EOM calculations. Any set of 2N basis operators, satisfying certain conditions, provides the exact EOM energies which are equivalent to complete configuration interaction results within the same orbital basis. We investigate the use of particle-particle shifting operators which are not employed in EOM calculations in model calculations on He with operator bases smaller than the complete 2V to consider the convergence of the expansion. The dependence of EOM calculations on the quality of the approximate ground state wavefunction is studied through calculations for Be where additional support is provided for the frequent need for multiconfigurational zeroth order reference functions (as corrected perturbatively). Excited state EOM wavefunctions from EOM calculations are shown to not necessarily be orthogonal to either the exact or approximate ground state wavefunction, suggesting implications in the use of EOM methods to evaluate excited state properties. The He and Be examples and a simple two-level problem are also utilized to illustrate questions concerning the use of the EOM equations to obtain an iteratively improved ground state wavefunction.     

Spectroscopy of complex molecules in the gas phase

A brief review is presented of theoretical and experimental research into the role of statistical factors in the formation of the characteristics of absorption and emission processes of light, observed for low-density and rarefied vapours of complex molecules. It is shown, in particular, that the average energy of molecules excited per unit time differs from the mean energy of molecules in the ground state, not by the energy of the exciting photon hv, but by the sum of hv and the selective energy which is the result of different absorption probabilities for molecules of different energy. This correction is the most important in rotational—vibrational absorption bands. This was established when the selective energy was calculated using the experimental data with the help of the formulae obtained. Average energies of the initial and final combining states reduced by the average energy of molecules in the ground state are calculated. Correlation curves similar to those of Condon are plotted according to the calculated data. The electron transition frequencies and the identities of absorption and emission transitions are determined through these curves; whereas for rotational—vibrational bands the value of the rotational constant and the variation of the latter upon excitation are estimated.     

Behavior of radical ion pairs produced by photoinduced electron transfer in polar solutions : Their dynamics in picosecond-hundred nanosecond regime

The dynamic behavior of radical ion pairs in polar solvents has been studied by directly observing time-resolved transient absorption spectra in the picosecond-hundred nanosecond regime and also by observing the picosecond laser induced photocurrent. Pyrene-N.N-dimethylaniline, pyrene-p-dicy-anobenzene, pyrene-triethylamine exciplex systems and the excited state of pyrene-pyromellitic dian-hydride electron donor-acceptor complexes in polar solvents have been examined. It has been clearly demonstrated that the rate constant k_n, of the charge recombination deactivation of radical ion pairs shows a strong dependence upon the energy gap ΔG_ip, (between the ion pair and the neutral ground state) and upon the molecular nature of individual electron donor or acceptor ions. The plot of k_nvs ΔG_ip for the chemically similar π-π exciplex systems as well as singlet excited electron donor-acceptor complex systems studied in this and some previous works showed clearly the characteristic features of the so-called Marcus inverted region.     

Theoretical study of the electronic spectrum of diimide by AB initio methods

A series of ab initio calculations is reported for the ground and low-lying valence and Rydberg states of diimide N₂H₂. Symmetric bending potential curves for both the cis and trans forms of this system have been obtained at the SCF level of treatment. In addition Cl calculations have been carried out for the trans-diimide ground state equilibrium nuclear conformation, using a configuration selection procedure described elsewhere; an associated energy extrapolation scheme is also employed which enables the effective solution of secular equations with orders of up to 40000. The ensuing Cl wavefunctions are interpreted in the discussion and the corresponding calculated energy differences between the various electronic states are compared with experimental transition energy results for both diimide and for related systems such as trans-azomethane. A more detailed analysis of the observed absorption bands in the ¹B_g-X¹A_g transition in N₂H₂ is also given, making use of calculated potential curve data as well as the pertinent Cl vertical energy difference. The dipole-forbiddenness of the excitation process is thereupon concluded to result in a distinct non-verticality for this electronic band system, causing its absorption maximum to occur at a position some 0.6 eV to the blue of the so-called vertical transition, i.e., that for which maximum vibrational overlap is obtained.     

Molecular orbital study of cobalt-oxygen interaction

A modified CNDO-UHF procedure is used to discuss cobalt-oxygen interactions in CoO and [CoO₂]^q (q = −1, 0, +1, +2, +3). The cobalt orbitals that contribute most to the bonding in these systems are the 4s and 3d orbitals with relatively little contribution from the 4p orbitals. The ground state of CoO is calculated to be a²π with a π hole localized in the 3d orbitals. The dioxygen activation in the CoO₂^q systems is described in terms of the local electron configuration of the O₂(π) antibonding orbitals together with the charge, Mulliken bond order and bond length of coordinated O₂. The distortion properties are described in terms of the thermodynamic stability difference and the energy barrier for the peroxo to superoxo transformation. The CoO₂ systems studied were classified into two groups depending on the degree of dioxygen activation and distortion properties. The lowest activation energy calculated to break the O-O bond corresponded to 69 kcal mol⁻¹, suggesting that dissociative chemisorption of O¹ on a single Co atom is not a likely process.     

Experimental investigation of excited state electron transfer reactions between some bicyclic molecules and tetracyanoquinodimethane (TCNQ)

Investigations on photoinduced electron transfer (ET) reactions between excited (ground) bicyclic electron donors 5,6,7,8-tetrahydro-2-naphthol (TH2N), 2-methoxy-5,6,7,8-tetrahydro naphthalene (2MTHN) and ground state (excited) acceptor tetracyanoquinodimethane (TCNQ) in fluid solutions of different polarity at the ambient temperature (300 K) by electronic absorption, steady state fluorescence and time-resolved spectroscopic methods in the time domain of nanosecond order have been carried out. It is suggested that in highly polar solvent acetonitrile (ACN), a loosely-structured transient geminate ion-pair complex (GIP) in the excited singlet state (S₁) is formed due to the ET encounter between the present donor TH2N or 2MTHN and TCNQ and this GIP complex rapidly dissociates into stable excited radical ions, as evidenced from steady state spectra. In polar DMF solvents, TCNQ exhibits an electronic absorption band of its anion without the presence of donor molecules. Both steady state and time-resolved data indicate that ET reactions between the present donors and acceptor TCNQ are largely impeded in the less polar solvent tetrahydrofuran (THF). In the highly polar solvent ACN, ET reactions between the donors and acceptor TCNQ have been suggested to be of adiabatic or intermediate between adiabatic and non-adiabatic types, from the observation of radical ion species in the electronic excited state. For some bicyclic donors and TCNQ acceptor systems, large negative ΔG, which is a measure of the gap between locally excited and radical ion-pair states, shows reaction occurs in highly exothermic regions. Further observations of −ΔG>λ, nuclear reorganization energy parameters and the decrement of ET rate (k_ET) with increasing exothermicity (more negative ΔG values) suggest the ET reaction for the bicyclic donor—TCNQ acceptor systems studied in the present investigation might occur in the Marcus inverted region. The possibility of building up efficient photoconducting materials with the present donor acceptor systems is suggested.     

Projected BCS Tamm-Dancoff method for molecular electronic structures

A new Tamm–Dancoff method for the ground and excited states of molecular electronic systems is developed. The method begins with a number-projected BCS (PBCS ) wave function and is generated by excitations of particle pairs from the degenerate geminals in the PBCS wave function. A direct optimization of the PBCS wave function is accomplished with successive Bogoliubov transformations so that one-pair excitation terms in the Tamm-Dancoff expansion of the ground state vanish (the generalized Brillouin theorem). The spin-symmetry adapted first- and second-order Tamm–Dancoff bases and matrix elements are calculated by means of the CI expansion of the PBCS wave function with natural orbitals that diagonalize the BCS geminal matrix. Numerical calculations are presented for the H₄ system with D_2h and D_4h conformations and for methylene. The PBCS wave function is not a very good approximation for the ground state, accounting for only about half of the correlation energy. The second-order Tamm–Dancoff correction improves the result as much as the double excitation CI . The Tamm–Dancoff terms consisting of two triplet pairs coupled to a singlet, and those relaxing the constraint imposed on the pairwise excitations in the PBCS wave function are important.     

Radial and angular correlation in heliumlike ions

In the framework of nonrelativistic variational formalism a new type of basis set is proposed, to estimate separately the effect of radial and angular correlations on the ground‐state energy for helium isoelectronic sequence H^? to Ar¹⁶⁺. Effect of radial correlation is incorporated by using multiexponential functions arising from product basis sets suitably formed out of Slater‐type one‐particle orbitals. The angular correlation can be switched on by incorporating an expansion in terms of basis involving interparticle coordinates. With a set of six‐term Slater‐type one‐particle basis and five‐term interparticle expansion, the ground‐state energy of helium is estimated as ?2.9037236 (a.u.) compared with the multiterm variational estimates ?2.9037244 (a.u.) due to Pekeris and Thakkar and Smith and Drake. Matrix elements of different operators in the ground state have been calculated and found to be in good agreement with available accurate results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

An investigation of the two electron chemical bond calculating energy expectation values from density matrix partitionings. II. The heteronuclear case HeH+

Bond energy contributions calculated from first and second order density matrix terms as partitioned by Ruedenberg's procedure have been obtained for HeH⁺ in the ground state and in the first excited 1Σ⁺. For the chemically bonded ground state the full partitioning is investigated for all internuclear distances R. The wavefunctions used for calculating the density matrices are obtained from an SCF calculation at near Hartree-Fock quality, using Slater orbitals with exponents which for each R are optimized simultaneously with the coefficients. For the excited state a limited CI has been performed. The results for promotional, charge transfer, and interference terms for kinetic and potential bond contributions are presented in the form of energy plots E(R). Starting from the promoted atoms and subsequently allowing for charge transfer the importance of the electron interaction is demonstrated by the unusually low quasiclassical electron repulsion curve due to electronic charge transfer, which makes an essential contribution to the decrease in energy during bond formation.     

Steps toward a high precision evaluation of the hyperfine interactions in neutral muonic helium

The solution of the Schrödinger equation of the neutral muonic helium is sketched by an eigenfunction expansion method: the eigenfunctions of the two Coulombic centres problem (of chargesZ ₁=2,Z ₂=–1) are used to expand the wave function. Our Born expansion method is a generalization of the Born-Oppenheimer approximation to a system in which the two centres (He, ^–) do not have a stable equilibrium distance. The adiabatic approximation is solved, upper-lower bounds on the eigenvalue are given for a number of states. The hyperfine energy corrections are calculated in general terms and are given numerically for the ground state and for the first muonically and electronically excited states in the frames of the adiabatic approximation. Our best value fails to give the observed hyperfine splitting of the ground state by some 5 × 10^–4 (2 MHz).     

Reactivity of collisionally activated dichlorocarbene dications studied by tandem mass spectrometry

The dissociation mechanisms of dichlorocarbene dications following collisional activation have been investigated via tandem mass spectrometric techniques and semi-empirical calculations. Three channels appear to be significant: {fx1019-1} The second channel becomes dominant at high internal energy. Production of ground state fragments (channel 1) involves a transition driven by spin—orbit coupling from the CCl ₂ ²⁺ $CCl_2^2 \tilde X^1 \Sigma _g^ + $ state to the CCl ₂ ^2? ā³Σ _u ^? state en route to the fragments. The dissociation barrier for the production of ground state fragments from the ground electronic state of CCl ₂ ²⁺ via the spin—orbit-induced transition is equal to 420 kJ mol^?1. The dissociation pathway that corresponds to channel 3 includes a first isomerization step from the linear Cl-C-Cl²⁺ structure to a bent Cl-Cl-C²⁺ connectivity. The calculated isomerization barrier amounts to 550 kJ mol^?1. The calculated reverse activation barriers are compatible with the measured kinetic energy released on the fragments.     

A quasipotential theory for the relativistic hydrogen atom

Using a previously described relativistic quantum theory for two particles, the spectrum is calculated of an electron with spin 1/2, which is bound by Coulomb interaction to a spinless point nucleus of finite mass and chargeZe. Only states with positive energy are used in the theory. The spectrum is calculated to order α⁴ and includes recoil effects. In the static limit it coincides with the spectrum as calculated by the Dirac equation. Terms of order α⁵ lift the degeneracy between the 2S _1/2 and 2P _1/2 states. The critical valueZ _cr of the nuclear charge above which the 1S _1/2 state gets a binding energy larger than twice the mass of the electron, is found to be 142. This value will increase when also the nuclear structure is taken into account.     

Chemical deposition of semiconducting cadmium selenide quantum dots in thin film form and investigation of their optical and electrical properties

Cadmium selenide quantum dots with cubic crystal structure are chemically deposited in thin film form using selenosulfate as a precursor for selenide ions and ammonia buffer with double role: as a ligand and as a pH value controller. The optical band gap energies of as-deposited and thermally treated cadmium selenide thin films, calculated within the framework of parabolic approximation for the dispersion relation, on the basis of equations which arise from the Fermi's golden rule for electronic transitions from valence to conduction band, are 2.08 and 1.77 eV, correspondingly. The blue shift of band gap energy of 0.34 eV for as-deposited thin films with respect to the bulk value is due to the quantum size effects (i.e., nanocrystals behave as quantum dots) and this finding is in agreement with the theoretical predictions. During the thermal treatment the nanocrystals are sintered, the increase of crystal size being in correlation with the decrease of band gap energy. The annealed thin films are practically non-quantized. From the resistance-temperature measurements, on the basis of the dependence of ln(R/Ω) vs 1/T in the region of intrinsic conduction, the thermal band gap energy (at 0 K) of 1.85 eV was calculated.     

High‐spin behavior of molecular crystals and extended π systems

The qualitative rules for the existence of high‐spin ground states in extended systems and molecular crystals are examined here on a firmer theoretical footing. Extended systems have been categorized into three groups, namely, type I, type II, and type III, depending on the type of bonding interactions. The general form of the spin Hamiltonian operators have been written down. The active spaces have been restricted to the minimum size for each of these three types of spin systems. The zeroth‐order state vectors and the Hartree–Fock ground‐state energies have been identified for unit species of each type. The extended system Hamiltonian operators are further truncated in such a way that only the nearest‐neighbor interactions are retained. Expressions have been derived for the energy gap from a molecular orbital approach. The relatively small effects of electron correlation on the energy gaps have been estimated for the type I systems, which belong to the systems of solid‐state physics. In particular, it has been shown that for the type I systems the singlet–triplet gap, and hence the ferromagnetic coupling constant, primarily depends upon the difference of one‐electron kinetic energies and not on the two‐electron exchange integrals. This result agrees with the concept of kinetic exchange that was introduced in the context of a resonating valence‐bond formalism. Type II systems are exemplified by extended systems that can be prepared from conjugated molecules while organic molecular crystals form examples of type III species. For these systems, however, the Coulomb exchange interaction has been shown to dominate the energy gap. A quick review of the Heisenberg spin Hamiltonian for the H₂ molecule is sufficient to point out that the sign of the calculated ferromagnetic coupling constant depends on the method of calculation, the nature of the basis set, and the bond length. This is amply supported by ab initio calculations on this species. Numerical data have also been obtained from computations on m‐phenylene‐coupled nitroxy radicals and stacks of α‐nitronyl nitroxide, but these calculations have been based on a semiempirical quantum chemical methodology (INDO) since some of the species involved are exceedingly large. Computed energy gaps are in good agreement with experimental and other theoretical (AM1, PM3) results. Nevertheless, for the dimer, trimer, tetramer, and pentamer of the type II specimen, the important π orbitals are far from being degenerate. The quantitative results clearly deviate from the criterion of degeneracy that was suggested from qualitative theories for the existence of a high‐spin ground state. Therefore, the criteria for the existence of high spins have been reformulated in terms of the monomer orbitals. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 308–324, 2000     

Predicting phosphorescence energies and inferring wavefunction localization with machine learning

Phosphorescence is commonly utilized for applications including light-emitting diodes and photovoltaics. Machine learning (ML) approaches trained on ab initio datasets of singlet–triplet energy gaps may expedite the discovery of phosphorescent compounds with the desired emission energies. However, we show that standard ML approaches for modeling potential energy surfaces inaccurately predict singlet–triplet energy gaps due to the failure to account for spatial localities of spin transitions. To solve this, we introduce localization layers in a neural network model that weight atomic contributions to the energy gap, thereby allowing the model to isolate the most determinative chemical environments. Trained on the singlet–triplet energy gaps of organic molecules, we apply our method to an out-of-sample test set of large phosphorescent compounds and demonstrate the substantial improvement that localization layers have on predicting their phosphorescence energies. Remarkably, the inferred localization weights have a strong relationship with the ab initio spin density of the singlet–triplet transition, and thus infer localities of the molecule that determine the spin transition, despite the fact that no direct electronic information was provided during training. The use of localization layers is expected to improve the modeling of many localized, non-extensive phenomena and could be implemented in any atom-centered neural network model.

We address phosphorescence, a localized phenomenon, by building localization layers into a DNN model of singlet–triplet energy gaps. These layers improve model performance and simultaneously infer the location of spin excitations within molecules.     

Full potential study of the elastic, electronic, and optical properties of spinels MgIn2S4 and CdIn2S4 under pressure effect

The structural, elastic, electronic, and optical properties of cubic spinel MgIn₂S₄ and CdIn₂S₄ compounds have been calculated using a full relativistic version of the full-potential linearized-augmented plane wave with the mixed basis FP/APW+lo method. The exchange and correlation potential is treated by the generalized-gradient approximation (GGA). Moreover, the Engel-Vosko GGA formalism is also applied to optimize the corresponding potential for band structure calculations. The ground state properties, including the lattice constants, the internal parameter, the bulk modulus, and the pressure derivative of the bulk modulus are in reasonable agreement with the available data. Using the total energy-strain technique, we have determined the full set of first-order elastic constants C_ij and their pressure dependence, which have not been calculated or measured yet. The shear modulus, Young’s modulus, and Poisson’s ratio are calculated for polycrystalline XIn₂S₄ aggregates. The Debye temperature is estimated from the average sound velocity. Electronic band structures show a direct band gap (Г-Г) for MgIn₂S₄ and an indirect band gap (K-Г) for CdIn₂S₄. The calculated band gaps with EVGGA show a significant improvement over the GGA. The optical constants, including the dielectric function ε(ω), the refractive index n(ω), the reflectivity R(ω), and the energy loss function L(ω) were calculated for radiation up to 30 eV.