The Internuclear Separation Derivatives of the Energy of a Diatomic Molecule
Hellman-Feynman theorem used for internuclear separation derivatives of diatomic molecule energy
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Hellman-Feynman theorem used for internuclear separation derivatives of diatomic molecule energy
The existence of gaseous BeH 2 , predicted from simple valence theory, has still not been established experimentally. We have estimated the total energy of this molecule, assumed linear symmetric, as the sum of four negative terms; the calculated SCF energy, the SCF error to the Hartree-Fock limit, the correlation energy to the exact nonrelativistic energy, and the relativistic energy.
For nearly 40 yr, studies of exosphere formation on airless bodies have been hindered by uncertainties in our understanding of the underlying ion collisional sputtering by the solar wind (SW). These ion impacts on airless bodies play an important role in altering their surface properties and surrounding environment. Much of the collisional sputtering data needed for exosphere studies come from binary collision approximation (BCA) sputtering models. These depend on the surface binding energy (SBE) for the atoms sputtered from the impacted material. However, the SBE is not reliably known for many materials important for planetary science, such as plagioclase feldspars and sodium pyroxenes. BCA models typically approximate the SBE using the cohesive energy for a monoelemental solid. We use molecular dynamics (MD) to provide the first accurate SBE data we are aware of for Na sputtered from the above silicate minerals, which are expected to be important for exospheric formation at Mercury and the Moon. The MD SBE values are ∼8 times larger than the Na monoelemental cohesive energy. This has a significant effect on the predicted SW ion sputtering yield and energy distribution of Na and the formation of the corresponding Na exosphere. We also find that the SBE is correlated with the coordination number of the Na atoms within the substrate and with the cohesive energy of the Na-bearing silicate. Our MD SBE results will enable more accurate BCA predictions for the SW ion sputtering contribution to the Na exosphere of Mercury and the Moon.
Most of the important chemical reactions which occur in the very high temperature air produced around space vehicles as they enter the atmosphere were investigated both experimentally and theoretically, to some extent at least. One remaining reaction about which little is known, and which could be quite important at the extremely high temperatures that will be produced by the class of space vehicles now contemplated - such as the AOTV - is the excitation of bound electron states due to collisions between heavy gas particles. Rates of electronic excitation due to free electron collisions are known to be very rapid, but because these collisions quickly equilibrate the free and bound electron energy, the approach to full equilibrium with the heavy particle kinetic energy will depend primarily on the much slower process of bound electron excitation in heavy particle collisions and the subsequent rapid transfer to free electron energy. This may be the dominant mechanism leading to full equilibrium in the gas once the dissociation process has depleted the molecular states so the transfer between molecular vibrational energy and free electron energy is no longer available as a channel for equilibration of free electron and heavy particle kinetic energies. Two mechanisms seem probable in electronic excitation by heavy particle impact. One of these is the collision excitation and deexcitation of higher electronic states which are Rydberg like. A report, entitled 'Semi-Classical Theory of Electronic Excitation Rates', was submitted previously. This presented analytic expressions for the transition probabilities, assuming that the interaction potential is an exponential repulsion with a perturbation ripple due to the dipole-induced dipole effect in the case of neutral-neutral collisions, and to the ion-dipole interaction in the case of ion-neutral collisions. However the above may be, there is little doubt that excitation of ground state species by collision occurs at the point where the initial and final potentials cross, or at least come very close. Therefore, this mechanism would be applicable to the case where a gas is initially at very low temperature suddenly subjected to high energy heavy particle bombardment. This situation would model the measurement of excitation cross section by molecular beam techniques, for example. The purpose is to report values of cross sections and rate coefficients for collision excitation of ground state atoms estimated with the Landau-Zener transition theory and to compare results with measurement of excitation cross sections for a beam of Hydrogen atoms impacting Argon atom targets. Some very dubious approximations are used, and the comparison with measurement is found less than ideal, but results are at least consistent within order of magnitude. The same model is then applied to the case of N-N atom collisions, even though the approximations then become even more doubtful. Still the rate coefficients obtained are at least plausible in both magnitude and functional form, and as far as I am aware these are the only estimates available for such rate coefficients.
Ground state energy of molecule in adiabatic approximation
The environments experienced by vehicles upon entry into planetary atmospheres generally result in severe aerothermodynamic loading. These flows are characterized by the formation of strong shock waves, behind which high temperatures and non-equilibrium environments are generated, and the accurate prediction of internal energy relaxation and chemical kinetics becomes important. This manuscript focuses on the internal relaxation of the rotational energy of polyatomic molecules. Previous work has described the implementation of a discrete rotational energy model for diatomic molecules (linear rotators). Later, Gimelshein et. al extended this model to include polyatomic molecular internal energies. However, they did not include details on how to generate the particles at equilibrium conditions and centrifugal distortion was not included in their model. The purpose of the present study is to extend the afore-mentioned models to the treatment of discrete rotational energy in polyatomic molecules with the addition of centrifugal distortion. An overview of the background theory needed for the implementation of the model will be given followed by the model itself and verification of the model. For example, sampled versus Boltzmann distributions are compared in Figure 1 for CH3 (oblate rotator – two quantum numbers) and examples of thermal relaxation behavior for linear and non-linear rotators are presented in Figure 2. In addition, comparisons of thermophysical properties will be presented, as well as examples of adiabatic relaxation and application to hypersonic flow.
The variational quantum eigenvalue solver is a powerful hybrid quantum-classical approach that has been suggested as a candidate method to run on near-term quantum hardware for computing ground state electronic energies of molecular systems. However, even for small molecules, the number of variational parameters and qubits required to minimize the electronic energy is beyond the reach of current quantum computers except for small basis sets. We explore a new paradigm for state preparation where we test how much of the optimization can be approximately prepared with classical computers to reduce the number of optimization steps performed using a quantum device. By adapting a recent algorithm for the factorized form of the UCC ansatz, we can study molecular electronic structure problems with up to 64 qubits. In addition, we also test a related approach of using tensor networks to optimize quantum circuits in order to benchmark various lattice models. We present results using these approaches and discuss strategies for incorporating these ideas into variational algorithms involving near-term quantum computers. Our results help demonstrate the strength of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction.
The purpose is to attempt a general introduction to pulsed carbon dioxide lasers of the kind used or proposed for laser radar applications. Laser physics is an excellent example of a cross-disciplinary topic, and the molecular spectroscopy, energy transfer, and plasma kinetics of the devices are explored. The concept of stimulated emission and population inversions is introduced, leading on to the molecular spectroscopy of the CO2 molecule. This is followed by a consideration of electron-impact pumping, and the pertinent energy transfer and relaxation processes which go on. Since the devices are plasma pumped, it is necessary to introduce a complex subject, but this is restricted to appropriate physics of glow discharges. Examples of representative devices are shown. The implications of the foregoing to plasma chemistry and gas life are discussed.
Extended average energy approximation of first order perturbation wave function, proposing procedure for multidimensional problems
The delta-ray theory of track structure is compared with experimental data for the radial dose from heavy ion irradiation. The effects of electron transmission and the angular dependence of secondary electron ejection are included in the calculations. Several empirical formulas for electron range and energy are compared in a wide variety of materials in order to extend the application of the track-structure theory. The model of Rudd for the secondary electron-spectrum in proton collisions, which is based on a modified classical kinematics binary encounter model at high energies and a molecular promotion model at low energies, is employed. For heavier projectiles, the secondary electron spectrum is found by scaling the effective charge. Radial dose calculations for carbon, water, silicon, and gold are discussed. The theoretical data agreed well with the experimental data.
Energy of interaction between two hydrogen atoms in their ground states described by Gauss-type functions
Projected requirements for efficient, economical, orbit-raising propulsion systems have generated investigations into several potentially high specific impulse, moderate thrust, advanced systems. One of these systems, laser thermal propulsion, utilizes a high temperature plasma as the enthalpy source. The plasma is sustained by a focused laser beam which maintains the plasma temperature at levels near 20,000 K. Since such temperature levels lead to total dissociation and high ionization, the plasma thruster system potentially has a high specific impulse decrement due to recombination losses. The nozzle flow is expected to be sufficiently nonequilibrium to warrant concern over the achievable specific impluse. This investigation was an attempt at evaluation of those losses. The One-Dimensional Kinetics (ODK) option of the Two-Dimensional Kinetics (TDK) Computer Program was used with a chemical kinetics rate set obtained from available literature to determine the chemical kinetic energy losses for typical plasma thruster conditions. The rates were varied about the nominal accepted values to band the possible losses. Kinetic losses were shown to be highly significant for a laser thermal thruster using hydrogen. A 30 percent reduction in specific impulse is possible simply due to the inability to completely extract the molecular recombination energy.
Approximation method using sum rules for energy shift in atomic system due to interaction of electrons with vacuum electromagnetic field applied to hydrogen, helium and lithium atom ground states and hydrogen molecule
We have recently estimated the total energy of the BeH 2 molecule as -15.918 ± 0.015 au. One of the steps in the analysis was to estimate the difference between the SCF energies computed with a minimal basis set of Slater orbits and with the best possible single-determinant wave function, the so-called Hartree-Fock limit and was predicted to be -15.773 ± 0.007 au for BeH 2 .
Total energy distribution measurements of field emitted electrons detect molecular infrared spectra of adsorbed molecules. Tunneling electron gives up energy to excite various modes of adsorbed molecule. These electrons, when energy-analyzed, show up on the collector and exhibit the spectra of various modes excited by tunneling electrons.
Rayleigh-Schroedinger perturbation calculations for ground state of diatomic hydrogen molecular ion
Perturbation theory of constrained variational method in molecular quantum mechanics
Internal and vibrational partition functions of carbon dioxide and rotational line intensities arising from transitions from ground and first excited states