Construction Of Potential Energy Curves Research Articles

Collision integrals of electronically excited atoms in air plasmas. I. N–N and O–O interactions

The current work presents the collision integral data for N(4 S)–N(4 S, 2 D, 2 P) and O(3 P, 1 D, 1 S)–O(3 P, 1 D, 1 S) interactions in the temperature range of 500–50 000 K. The collision integrals are calculated based on high-quality potential energy curves (PECs) obtained from fitting the high-level calculation data in a wide energy range to the neural network (NN) functions. In the construction of PECs, the diabatic PECs are adopted when avoided crossings exist because the diabatic paths are much more likely to be followed for such situations. Moreover, the nonadiabatic transition effects are estimated to be negligible for PECs crossings. The accuracy of traditional analytical formulas to fit PECs are also examined. It is found that the collision integral calculations are sensitive to the accuracy of PECs and the NN based PECs overwhelm the others. The contribution of inelastic excitation exchange processes to the diffusion collision integrals are also computed by using an accurate evaluation of the differences of PECs for gerade and ungerade pairs of excited atoms. Finally, based on the new collision integral data, we calibrate the collision model parameters suitable for the widely used particle simulation methods. The collision integrals and collision models developed in this work can be used to support high-confidence simulations of weakly ionized air plasma problems.

Electronic states, spectroscopic properties, electronic transitions, and bonding in ScH2+: A thermodynamic stable transition metal-hydrogen dication

Eight bound singlet and triplet electronic states of the diatomic dication ScH2+ are characterized theoretically at the SA-CASSCF/icMRCI/aug-cc-pV5Z level of theory by the construction of potential energy curves, and the evaluation of spectroscopic parameters. The states dissociating into the first channel are all thermodynamically stable. For the ground state, covalent bonding plays a relevant role in the stabilization of the molecule; for the other states, bonding results mainly from electrostatic charge-induced dipole interaction. Dipole moment (relative to the center of mass) functions and vibrationally averaged dipole moments quantify the polarity of the molecule. After evaluating transition moment functions, transition probabilities for spontaneous emission for selected pair of states are estimated by the Einstein Av´,v´´ coefficients and the stronger transitions identified; radiative lifetimes are also reported. Not yet known experimentally, this work is expected to motivate experimental investigations of transition metal-monohydrides diatomic dications.

Characterizing electronic states in metal-rare gas diatomic dications: The cases of VAr2+ and VKr2+

Six low-lying bound quartet electronic states of the diatomic dications VAr2+ and VKr2+ are characterized theoretically at the SA-CASSCF/icMRCI/aug-cc-pV5Z level of theory by the construction of potential energy curves, and the evaluation of spectroscopic parameters. These molecules were found to be thermodynamically stable, where binding arises from purely electrostatic charge-induced dipole interaction; they are more strongly bound than the corresponding monocations. Their polarity is described by dipole moment functions and vibrationally averaged dipole moments. Transition probabilities for spontaneous emission for selected pair of states are estimated by the Einstein Av′v′′ coefficients and the stronger transitions identified; radiative lifetimes are also reported. Not yet known experimentally, this work is expected to motivate further experimental investigations of transition metal-rare-gas diatomic dications.

Electronic Structure of RhO2+, Its Ammoniated Complexes (NH3)1-5RhO2+, and Mechanistic Exploration of CH4 Activation by Them.

High-level electronic structure calculations are initially performed to investigate the electronic structure of RhO2+. The construction of potential energy curves for the ground and low-lying excited states allowed the calculation of spectroscopic constants, including harmonic and anharmonic vibrational frequencies, bond lengths, spin-orbit constants, and excitation energies. The equilibrium electronic configurations were used for the interpretation of the chemical bonding. We further monitored how the Rh-O bonding scheme changes with the gradual addition of ammonia ligands. The nature of this bond remains unaffected up to four ammonia ligands but adopts a different electronic configuration in the pseudo-octahedral geometry of (NH3)5RhO2+. This has consequences in the activation mechanism of the C-H bond of methane by these complexes, especially (NH3)4RhO2+. We show that the [2 + 2] mechanism in the (NH3)4RhO2+ case has a very low energy barrier comparable to that of a radical mechanism. We also demonstrate that methane can coordinate to the metal in a similar fashion to ammonia and that knowledge of the electronic structure of the pure ammonia complexes provides qualitative insights into the optimal reaction mechanism.

Characterizing electronic states and spectra in transition metal-rare gas diatomic cations: The cases of VAr+ and VKr+

Nine low-lying quintet electronic states of the cations VAr+ and VKr+ are characterized theoretically at the SA-CASSCF/icMRCI/aug-cc-pV5Z level of theory by the construction of potential energy curves and the determination of spectroscopic parameters. The polarity of the molecules is described by dipole moment functions and vibrationally averaged dipole moments. Transition probabilities for spontaneous emission for selected states are estimated by the Einstein Av´,v´´ coefficients and the stronger transitions identified; radiative lifetimes are also reported. For the photoabsorption process, the spectrum is modelled for the bands of the G 5Π – X 5Σ+ system of each species for which experimental photodissociation results are available in the literature. Not known experimentally, the intensity distribution is expected to help elucidate the assumed vibrational numbering of the upper state, and together with the overall electronic description and spectroscopic parameters motivate further experimental investigations of transition metal-rare-gas cations. Binding arises from purely electrostatic charge-induced dipole interaction.

Applications of analytic continuation in the construction of potential energy curves

The representation of potential energy curves by continued fractions is investigated and shown to be a useful method in the extrapolation of data. A generalization of the method is presented that enables one to treat avoided crossing problems. Given data on one curve involved in the avoided crossing, it is possible to obtain a good approximation to the other. Results for various model calculations and for the H2 (E. F1Σ+θ) and CO (1Σ+) potential curves are presented.

Inverse problems in quantum chemistry

AbstractInverse problems constitute a branch of applied mathematics with well‐developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

CH2 revisited

The first four states of the CH2 molecule ([Formula: see text]3B1, ã1 A1, [Formula: see text]1A1, and [Formula: see text]1A1) are examined using state-of-the-art ab initio methods and basis sets. The construction of potential energy curves with respect to the C + H2 and CH + H channels provides significant clues to understanding the geometric and electronic structure of the above states. All of our numerical findings are in excellent agreement with the existing experimental data. Key words: CH2, MRCI, potential curves, vbL icons.

Theoretical study of photochemical processes involving singlet excited states of formaldehyde carbonyl oxide in the atmosphere

Abstract We report a theoretical study on the photochemical reactivity of formaldehyde carbonyl oxide H2COO, a compound of atmospheric relevance. Calculations are carried out at the CASSCF and CASPT2 levels with extended basis sets. We are particularly interested in three important unimolecular processes: isomerization into dioxirane, syn/anti isomerization and dissociation into formaldehyde and atomic oxygen. The results suggest that the photochemical reactivity of H2COO in the troposphere is strongly linked to the properties of the second singlet excited state a 1 A ′ ( π → π * ) because it is energetically accessible from the ground state and has a large oscillator strength. Construction of potential energy curves reveals that photochemical isomerization into dioxirane is very unlikely to occur whereas syn/anti isomerization should be favorable. Besides, in the a1A′ state, carbonyl oxide spontaneously dissociates into formaldehyde H2CO and atomic oxygen O ( 1 D ) in close relationship to the excited 1 B 2 state of the isoelectronic ozone molecule occurring in Hartley’s band.

Construction of potential curves for diatomic molecular states by the IPA method

A program package is presented which utilizes the Inverted Perturbation Approach (IPA) method for construction of potential energy curves of 1Σ and 1Π states of diatomic molecules directly from the experimental data. In most cases using the constructed IPA potential one can reproduce the experimental energy levels within the accuracy of measurement. The package is successfully tested in case of double minimum potential where the traditional RKR method is not applicable.

Ion-pairing and charge-transfer interactions between octacyano-molybdates(IV) and -tungstates(IV) and diquaternary bipyridines

New salts of formula [pq]2[M(CN)8] [M = Mo or W, pq = paraquat (1,1′-dimethyl-4,4′-bipyridinediium)] have been synthesized. The systems {A2+, M(CN)84–} where A2+ = pq or dq (diquat, 6,7-dihydrodipyrido[1,2-a∶2′,1′-c]pyrazinediium), which show optical electron transfer from anion to cation, were studied. The first association constants in aqueous solution were determined spectroscopically and the properties of the ion-pair charge-transfer bands were used for calculation of the thermodynamic parameters of the electron transfer and construction of potential-energy curves on the basis of the Hush model.

Construction of bound-state potential energy curves of diatomic molecules from spectroscopic data

We propose a method for the construction of potential energy curves of diatomic molecules from spectroscopic data. It is based on perturbation theory and an appropriate numerical integration algorithm and corrects the potential energy function iteratively until the eigenvalues of the Schrödinger equation agree with the experimental energies. The method is stable and converges fast enough to allow one to adjust many potential parameters. We choose the eigenvalues of the Kratzer oscillator as experimental data to test both the performance of the method and the accuracy of the Dunham expansion about equilibrium. The Dunham expansion obtained from the spectrum has a range of utility which is remarkably larger than the radius of convergence of the Taylor expansion about equilibrium. We also apply the present method to the ground electronic state of the CO molecule and show that the Dunham expansion agrees with the RKR turning points. We discuss further applications of the method.

Improving on the conventional presentation of molecular vibrations: Advantages of the pseudoharmonic potential and the direct construction of potential energy curves

Two improvements in the discussion of molecular vibrations are suggested. First, the pseudoharmonic potential possesses advantages over the harmonic: as a proper potential should, it has a larger force constant inside the equilibrium distance than outside and becomes infinite for zero distance. Its eigenvalues and eigenfunctions may be obtained in closed form either by the power series method or by manipulation of the Schrödinger equation into a standard form. Unlike the harmonic case, this is still true in the presence of a centrifugal potential. The second improvement involves a direct method of constructing a potential energy curve from the energy levels, rather than adjusting parameters in a potential so that calculated energy levels fit experimental values. The method, which involves the instructive semiclassical momentum, is illustrated for the harmonic and pseudoharmonic potentials, with an apparent paradox cleared up.

Theoretical Studies Related to Time Resolved Spectroscopy: The Iterative Rydberg-Klein-Dunham Method and Weyl Theory Applied to the Predissociations in the B2Σ- State of CH

The Iterative Rydberg-Klein-Dunham (IRKD) method for the construction of potential energy curves for diatomic molecules is applied to the B2Σ- state of the CH radical. Experimental information form all rovibronic bound states (and even some orbiting resonances) is used. Both spin components, F1 and F2, of the model potential are treated. The resulting curves accurately reproduce the input information and are used to calculate orbiting resonances by means of LeRoy and Bernstein's Airy function boundary condition method (where applicable) and by the Weyl-Titchmarsh-Riccati technique.For the orbiting resonances the calculated linewidths are compared with experimental lifetime measurements and the long range parts of the potential energy curves are adjusted to fit the lifetimes. Finally, an observed interaction between the B2Σ- and A2Δ state is discussed.

A compression method for measuring forces between colloidal particles

The repulsive force between colloidal particles as a function of separation distance has been estimated from measurements of the equilibrium pressures and volumes of a model latex confined between a semipermeable membrane and an immiscible liquid. The pressure-volume data obtained in experiments with electrostatically stabilized latices in salt solutions and in methanol provided a basis for construction of potential energy curves that compared well with theoretical predictions for two-particle interactions. Effects of steric repulsion were investigated in a polystyrene latex system stabilized with nonionic surfactants. It was found that the distance over which repulsion was detectable was not affected by an increase in the hydrophobic part of the chain when the hydrophilic part was unchanged. On the other hand, increases in length of the hydrophilic part with the hydrophobic one being constant, resulted in progressive extension of the steric barrier. The experimentally determined interaction forces were comparable to those theoretically predicted for short distances, but the total energy of repulsion was lower than expected.

Angular momentum coupling, potential curves and radiative selection rules for heavy diatomic molecules, with particular reference to Kr 2 and Kr 2+

The coupling of electronic orbital angular momentum, spin, and molecular rotation of diatomic molecules is summarized, with emphasis on heavy molecules where the spin-orbital interaction is not small. The symmetry properties of diatomic wavefunctions are discussed and tabulated. The building up of molecular electronic states from states of the separated atoms, from states of the united atom, and from molecular orbitals is also explained. These principles and other data are applied to the construction of potential energy curves for Kr 2 and Kr 2 +, following the example of Mulliken for Xe 2 and Xe 2 +. Finally, the electric dipole selection rules for radiative transitions between electronic states are summarized and applied to Kr 2.

Construction of potential energy curves in avoided crossing situations

A new means of analytic continuation, specifically designed to treat branch point structure, is introduced and applied to two-state avoided crossing models. By means of this method it is possible to obtain approximations to both curves using limited data from either curve or both curves. Further, the method provides a good analytic continuation into the complex plane and is able to accurately locate the complex branch points.