Triatomic Linear Molecules Research Articles

Electronic states and valley-orbit coupling in linear and planar molecules formed by coupled P donors in silicon

Using the effective mass theory and the multi-valley envelope function representation, we have developed a theoretical framework for computing the single-electron electronic structure of several phosphorus donors interacting in an arbitrary geometrical configuration in silicon taking into account the valley-orbit coupling. The methodology is applied to three coupled phosphorus donors, arranged in a linear chain and in a triangle, and to six donors arranged in a regular hexagon. The results of the simulations evidence that the valley composition of the single-electron states strongly depends on the geometry of the dopant molecule and its orientation relative to the crystallographic axes of silicon. The electron binding energy of the triatomic linear molecules is larger than that of the diatomic molecule oriented along the same crystallographic axis, but the energy gap between the ground state and the first excited state is not significantly different for internuclear distances from 1.5 to 6.6 nm. Three donor atoms arranged in a triangle geometry have larger binding energies than a triatomic linear chain of dopants with the same internuclear distances. The planar donor molecules are characterized by a strong polarization in favor of the valleys oriented perpendicular to the plane of the molecule. The polarization increases with number of atoms forming the planar molecule.

Application of the Padé approximations to calculation of rotational energies of a triatomic linear molecule

A possibility of applying the Pade approximations to calculation of rotational-level energies of degenerate vibrational states is studied for linear molecules with various quantum numbers of the vibrational angular momentum 1. The calculations of rotational energy levels for the CO 2 molecule show that the Pade form has a better predictability as compared to a power series. Spectroscopic constants of the Pade approximations for the vibrational states (0400, 0420, 0440), (1400, 1420, 1440), (1510, 1530, 1550), and (0600, 0620, 0640, 0660) for the CO 2 molecule are determined.

Density matrix for a triatomic linear molecule model.

We find the unitary operator for diagonalizing the Hamiltonian of a triatomic linear molecule. The unitary operator is expressed in a coordinate representation that brings convenience for deriving the density matrix \ensuremath{\rho}(${\mathrm{x}}_{1}$,${\mathrm{x}}_{2}$,${\mathrm{x}}_{3}$;${\mathrm{x}}_{1}^{\ensuremath{'}}$,${\mathrm{x}}_{2}^{\ensuremath{'}}$,${\mathrm{x}}_{3}^{\ensuremath{'}}$,\ensuremath{\beta}). The unitary transformation approach is simple because the derivation can be reduced to the calculation of two independent harmonic-oscillator density matrices and one free-particle density matrix. The average of the potential energy and the kinetic of the molecule is calculated by using the density matrix.

Perturbation theory to determine the stable isomer of triatomic linear molecules

AbstractThe electronegativity perturbation theory up to the fourth order has been used to study the preferred isomer of linear triatomic molecules. Systems with 10–16 valence–electron systems are discussed and our results are in good agreement with the experiment. The only exception is the isomers of PNO. The usefulness of the perturbation theory is briefly discussed. © 1993 John Wiley & Sons, Inc.

Squeezing in the triatomic linear molecule model revealed by virtue of the IWOP technique

For a typical triatomic linear molecule with different atomic masses one finds a unitary operator which is closely related to squeezing transformations caused by frequency jumps. The coordinate representation of the unitary operator is identified, which provides an alternative approach for calculating the wavefunction of internal motion of the molecule. The author also shows that the unitary operator is equivalent to a two-mode squeezing-rotating combination operator multiplied from the right by two single-mode squeezing operators. The discussion is mainly based on the technique of integration within an ordered product (IWOP) of operators.

Third order determination of the vibrational spectroscopic constants for a triatomic linear molecule affected by Fermi resonance

For a molecule affected by Fermi resonance, we establish, up to third order of approximation, the general formulae relating the spectroscopic constants to the mean value of the vibrational energy (in any Fermi polyad) and to the spacings of vibrational energy levels (in a Fermi diad or a Fermi triad).

Some remarks on the significant character of spectroscopic constants (triatomic linear molecules)

The influence of the H v term on the values of the other spectroscopic constants B v and D v has been analyzed. The questions specifically considered are: When is it necessary to introduce it in the fit to reproduce satisfactorily the wavenumbers for the rotational structure of a given vibration-rotation transition? Even though this constant is not a significant parameter ( H > 3 δH, δH being the standard deviation) is it necessary to introduce it for extrapolations to very high J values? As a result of these considerations, it has been possible to define an experimental; protocol to determine “correct” spectroscopic constants.

Correlation functions of the Π–Σ and the Σ–Σ vibration–rotation bands of a triatomic linear molecule mixed with dense rare gases

The degenerate and nondegenerate rotation–vibration bands of OCS mixed with rare gases have been scanned in the density range 15–300 amagat. The related correlation functions have been corrected for the hot band perturbations and compared with usual rotational models. None of the models fit both correlation functions. A comparison with experimental correlation functions arising from other linear molecules mixed with rare gases shows that a convenient rotational relaxation model would have to consider explicitly the mean square torque at least in the range of density explored. Such a requirement is fulfilled by using a memory function proposed by Steele. The correlation functions are then very well predicted for both vibrations using the same values of the parameters. The adjusted mean square torque values are then successfully compared with those determined directly by a spectral moment measurement method.

Orbital angular momentum in triatomic molecules

The effects of electronic angular momentum in triatomic linear molecules are considered. An effective vibronic hamiltonian is derived and second order energy level expressions are obtained for the bending levels in an electronic Π state. The formulae allow for the anharmonicity of the bending potentials and for the variation of the expectation value <Lz > with bond angle; effects of electron spins are also included. The vibronic levels predicted by the analytic expressions are compared with those calculated using a full matrix treatment of the orbital angular momentum; it is shown that they are far more accurate than the levels predicted by the formulae currently available in the literature. The relationship between the anharmonic corrections and the deviation of <Lz > from unity is discussed in terms of an electrostatic interaction between linear molecule states of different symmetry.

On some third-order corrections to the rotation-vibration energies of polyatomic molecules

After a review of the principles for calculating higher-order rotation-vibration energies of polyatomic molecules, the corrective terms of the third order are studied. Third-order effects are first considered in the absence of accidental resonances, and all the nonvanishing diagonal and nondiagonal elements that must be included in the matrix are calculated for molecules with axial symmetry, linear molecules and asymmetric molecules. The results obtained are applied to the study of the transitions J = 1 → 2 in an excited state v t = 1 ( l t = ±1) for molecules belonging to the symmetry group C 3 v . Comparison is made with the microwave spectrum of methylisocyanide in the excited state v 8 = 1. Next, two third-order effects in the presence of accidental resonances are studied: the Taylor-Benedict-Strong correction and the variation of the Fermi-resonance term with the quantum number J. It is shown in particular that the coefficient λ l of the Taylor-Benedict-Strong correction vanishes for a triatomic linear molecule, which is in excellent agreement with the experimental results obtained in the infrared spectrum of carbon dioxide.

Electronic Structures of Molecules XIV. Linear Triatomic Molecules, Especially Carbon Dioxide

Electron configurations of the triatomic linear molecules CO2, BO2—, N2O, CS2, COS, NO2+, N3—, NCO—, NCS—, BeF2, HgCl2, ClCN, ClBO, etc. are given. The electron configurations probably of all of these are formally analogous, or formally identical in the case of isoelectronic molecules, such as CO2, N2O, BeF2, etc. The BeH2 type is also touched on. The relations of the electron configurations to ordinary valence conceptions are discussed, and the importance in practice of cases intermediate between those represented by simple valence formulas is emphasized. The usefulness of the present method in giving a simple description of intermediate cases of all sorts (between double-bonded A=B=C and single-bonded A–B–C, between homopolar A–B–C, etc., and heteropolar A—B++C—, etc., between A–B≡C and A+=B=C—, etc.) is brought out. The ionization potentials of CO2, CS2, N2O, HgCl2 are interpreted in relation to their electron configurations. The minimum potentials of CO2, of CS2, and of HgCl2, respectively, correspond to removal of a nearly nonbonding pπ electron of the O, S, or Cl atom. It is shown that the ultraviolet emission bands of CO2 probably represent transitions among four electron states of CO2+ which correspond to the four lowest ionization potentials of CO2; if this interpretation of the bands is correct, the CO2+ molecule has a linear form in these states. According to this interpretation, the four lowest potentials of CO2 are probably 13.72, 17.09, 18.00, and about 21.5 volts (or perhaps 14.63, 18.00, 18.91, and about 22.4 volts). These values are based on identification of the CO2 Rydberg absorption series limit at 18.00 volts with one of the potentials. The minimum potential above obtained (13.72 or perhaps 14.63 volts) differs considerably from the accepted value 14.3 or 14.4 volts based on electron impact. Radicals N3, NCO, NCS, and molecules NO2 and others are also touched on. A reason for the triangular form of NO2 is found in the fact that linear NO2+ (like CO2 or N2 or NO+) is composed of a stable system of closed shells, while the final electron added to make neutral linear NO2 would have to go into a probably fairly high energy antibonding orbital (as in NO). Evidently the actual NO2 avoids this by being triangular. Ultraviolet absorption spectra of CO2, CS2, and COS are also considered.