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Introduction to Computational Methods in Organic Materials
Published in Sam-Shajing Sun, Larry R. Dalton, Introduction to Organic Electronic and Optoelectronic Materials and Devices, 2016
In the previous section, it has been shown how in a diatomic molecule the bonding and antibonding states arose. Now the consideration is generalized to a heteronuclear molecule [3]. The overlap integral will be still taken as a parameter β according to the notation β = H12 = H21. However, the on-site Hamiltonian matrix elements on the A and B atoms are now different, and the wave function of the molecule can be written in terms of the atomic states |A〉 and |B〉 as follows: () |Ψ〉=cA|A〉+cB|B〉.
Ideal Gases and Solutions
Published in Jeffrey Olafsen, Sturge’s Statistical and Thermal Physics, 2019
The case of the H2 molecule is interesting since its small moment of inertia produces a value of E0 of 7.5×10−3 eV, considerably larger than in any other gas. Furthermore, hydrogen remains gaseous down to a very low temperature (21 K at atmospheric pressure). At 50 K, kBT∼12E0 and CV drops significantly below 52R0. The rotational heat capacity of a heteronuclear molecule such as hydrogen deuterium (HD) is calculated in Problem 6.5 and shown as a function of temperature in Figure 6.7. Quantum mechanical effects arising from symmetry requirements on the nuclear wave function complicate the case of a homonuclear molecule,6 but the data on H2 are in qualitative agreement with that calculation.
Optical–optical double resonance process in free-jet supersonic expansion of van der Waals molecules: characteristics of the expansion, number of excited molecules and emitted photons
Published in Molecular Physics, 2022
Joanna Sobczuk, Tomasz Urbańczyk, Jarosław Koperski
Let us consider a process of formation of diatomic molecules (here MeAr from Me and Ar atoms), in a thermal equilibrium bath which takes place in the source nozzle According to Vigasin [20], near the bottom of the molecular potential that is well approximated by a truncated harmonic oscillator, equilibrium constant can be expressed in (atm−1) as where is a harmonic vibrational constant and is a rotational constant for a given υ, both in (cm−1), is the symmetry number (equal to 1 for heteronuclear molecule), is a nozzle stagnation temperature (equal to the temperature of a gas mixture in the crucible) in (K), is a reduced mass of MeAr in (atomic units) and De is MeAr ground-state potential depth in (K).
NMR Spectroscopy for Proof-of-Concept Experimentation on a Polarized Laser Fusion Process
Published in Fusion Science and Technology, 2022
Masahiko Utsuro, Mitsuo Nakai, Hideki Kohri, Takeshi Ohta, Takumi Konno, Asako Igashira, Mamoru Fujiwara
Polarization of heteronuclear molecules similar to heteronuclear hydrogen deuteride (HD) could be accomplished via the brute force method, where an HD target is acquired by employing polarized protons at 10 mK (Refs. 8 and 9). Although this method offers some clear advantages in terms of simplicity and ease of use, the brute force method is woefully lacking when it is applied for the polarization of D-T fusion experiments because of the excessive amounts of heat generated during the process that are caused by β-decay processes in the D-T target. We propose here another approach applicable to the case accompanying the β-decay processes in the D-T target, in which a ferromagnetic complex with a high internal magnetic field is used to polarize tritium nuclei on physisorbed D-T molecules. This paper discusses a series of experiments using the heteronuclear molecule HD, which is similar to D-T, and reports the experimental results. Other researchers have employed a different fusion reaction, namely, the D+3He→α+p reaction for generating polarized tokamak plasma as a means of circumventing the associated decay heat.10
Dissociation energy and the lowest vibrational transition in LiH without assuming the non-Born–Oppenheimer approximation
Published in Molecular Physics, 2022
Saeed Nasiri, Toreniyaz Shomenov, Sergiy Bubin, Ludwik Adamowicz
LiH, which is the smallest heteronuclear molecule, has only four electrons and it has been subject to meticulous theoretical calculations from the very early stages of quantum chemistry (see Table 13 in Ref. [2]). It has become a popular benchmark system for testing emerging quantum-mechanical methods for performing electronic-structure molecular calculations and for investigating the capability of the existing methods to produce more accurate results. In past decades, the LiH molecule has been studied using various high-level quantum mechanical methods such as configuration interaction (CI) [3–6], multi-reference configuration interaction (MR-CI) [3, 7–13], coupled-cluster (CC) [14–18] and explicitly correlated Gaussian functions (ECG) [19–24].