Helium: energies for singlets and triplets

2021 ◽  
pp. 178-190
Author(s):  
Geoffrey Brooker
Keyword(s):  
Variational Method ◽  
Wave Functions ◽  
Triplet States ◽  
Repulsion Energy ◽  
Electron Repulsion ◽  
Singlet States

“Helium: energies for singlets and triplets” discusses rival explanations as to why helium's triplet states lie below corresponding singlets. Computations reported in the literature show that triplet states have more compact wave functions than do corresponding singlet states, even though this makes the electron–electron repulsion energy larger for triplets. A simplified variational method is applied to an attempted calculation of the energies, but is inadequate, showing how helium is numerically unfriendly.

The molecular orbital theory of chemical valency. XII. The excited states of diatomic molecules

1953 ◽  
Vol 216 (1124) ◽  
pp. 1-10 ◽  
Keyword(s):  
Wave Equation ◽  
Excited States ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Wave Functions ◽  
Triplet States ◽  
Orbital Theory ◽  
Lennard Jones ◽  
Singlet States ◽  
Symmetry Properties

A method is developed for the solution of the wave equation for two electrons in the presence of two centres. The work of Lennard-Jones & Pople (1951) on the ground state of such a system is generalized so as to apply to all the excited states. Full advantage is taken of the symmetry properties of the wave functions, both in three-dimensional and six-dimensional space, to reduce the wave equation to a number of component parts, each of a particular symmetry type. This leads to sets of equations with characteristic symmetry properties appropriate to singlet states and triplet states, whether even or odd, positive or negative in the standard notation ( 1 ∑ - g ).

scholarly journals Theoretical Study of Thermal Cracking For Acenaphthylene Molecule

2013 ◽  
Vol 10 (3) ◽  
pp. 1071-1081
Author(s):  
Baghdad Science Journal
Keyword(s):  
Density Functional ◽  
Theoretical Study ◽  
Reaction Path ◽  
Polyaromatic Hydrocarbons ◽  
Thermal Cracking ◽  
Triplet States ◽  
Bond Energies ◽  
Functional Theory ◽  
Repulsion Energy ◽  
Bond Breakage

Density Functional Theory (DFT) calculations were carried out to study the thermal cracking for acenaphthylene molecule to estimate the bond energies for breaking C8b-C5a , C5a-C5 , C5-C4 , and C5-H5 bonds as well as the activation energies. It was found that for C8b-C5a , C5-C4 , and C5-H5 reactions it is often possible to identify one pathway for bond breakage through the singlet or triplet states. The atomic charges , dipole moment and nuclear – nuclear repulsion energy supported the breakage bond .Also, it was found that the activation energy value for C5-H5 bond breakage is lower than that required for C8b-C5a , C5a-C5 , C5-C4 bonds which refer to C5-H5 bond in acenaphthylene molecule are weaker than C8b-C5a , C5a-C5 , C5-C4 bonds .It is reasonable to presume that C5-H5 bonds are broken first when a acenaphthylene molecule is exposed to thermal cracking. It seems that the characteristic planarity for the polyaromatic hydrocarbons is an important factor to acquire the molecule structure of the required stability along the reaction path . The trends in the bond energies and the configuration structures are discussed .

A spectroscopic study of HCP, the phosphorus analogue of hydrocyanic acid

1969 ◽  
Vol 47 (8) ◽  
pp. 893-920 ◽  
Author(s):  
J. W. C. Johns ◽  
H. F. Shurvell ◽  
J. K. Tyler
Keyword(s):  
Energy Levels ◽  
Hydrocyanic Acid ◽  
Ultraviolet Absorption Spectrum ◽  
Triplet States ◽  
Fundamental Vibration ◽  
Excited Triplet ◽  
Singlet States ◽  
State Formula ◽  
Excited Singlet States ◽  
Vibration Rotation

The ultraviolet absorption spectrum of HCP has been observed from 4100 Å to about 2350 Å, and seven electronic transitions have been identified. Three of these transitions involve excited singlet states and four of them involve excited triplet states. The symmetries, energies, and equilibrium conformations of these states are listed below:[Formula: see text]Some observations have also been made on the vibration–rotation energy levels of the ground electronic state, [Formula: see text], of HCP. The fundamental vibration frequencies (in cm−1) are ν1 = 3216.9, ν2 = 674.7, and ν3 = 1278.4.

A variational method for calculating magnetic shielding constants in molecules

1957 ◽  
Vol 243 (1233) ◽  
pp. 264-273 ◽  
Keyword(s):  
Variational Method ◽  
Molecular Orbital ◽  
Diamagnetic Susceptibility ◽  
Valence Bond ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Magnetic Nucleus ◽  
Shielding Constants ◽  
Good Agreement

The general variational method is applied to the problem of calculating magnetic shielding constants in molecules. Using approximate variation functions together with simple molecular-orbital and valence-bond wave functions calculations have been made for the molecules hydrogen, methane, ethylene and acetylene. An approximation using the calculated diamagnetic susceptibility is used for electrons which are not localized near the magnetic nucleus considered. The results are in good agreement with experiment and in particular it is shown that the shielding constant for acetylene should lie between those for methane and ethylene.

Systematic construction of approximate one-matrix functionals for the electron-electron repulsion energy

2002 ◽  
Vol 117 (21) ◽  
pp. 9560-9566 ◽  
Author(s):  
Jerzy Cioslowski ◽  
Katarzyna Pernal ◽  
Paul Ziesche
Keyword(s):  
Systematic Construction ◽  
Repulsion Energy ◽  
Electron Repulsion

Electronic wave functions II. A calculation for the ground state of the beryllium atom

1950 ◽  
Vol 201 (1064) ◽  
pp. 125-137 ◽  
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
Accurate Result ◽  
Energy Criterion ◽  
Wave Functions ◽  
Exponential Functions ◽  
Approximate Wave Function ◽  
Electronic Wave Functions ◽  
Approximate Wave

An approximate wave function expressed in terms of exponential functions, spherical harmonics, etc., with numerical coefficients has been calculated for the ground state of the beryllium atom . Judged by the energy criterion this gives a more accurate result than the Hartree result which was the best previously known. This has been calculated as a trial of a fresh method of calculating atomic wave functions. A linear combination of Slater determinants is treated by the variational method. The results suggest that this will provide a more powerful and convenient method than has previously been available for atoms with more than two electrons.

scholarly journals Singlet Generation from Triplet Excitons in Fluorescent Organic Light-Emitting Diodes

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
A. P. Monkman
Keyword(s):  
Triplet States ◽  
Large Area ◽  
Major Drawback ◽  
Light Emitting ◽  
Light Emitting Devices ◽  
Singlet Exciton ◽  
Organic Light ◽  
Singlet States ◽  
Very High ◽  
Triplet Excitons

A potential major drawback with organic light-emitting devices, (OLEDs) is the limit of 25% singlet exciton production through spin-dependent charge recombination. Recent device results, however, show that this limit does not hold and far higher efficiencies can be achieved in purely fluorescent-based systems (Wohlgenannt et al. (2001), Dhoot et al. (2002), Lin et al. (2003), Wilson et al. (2001), Cao et al. (1999), Baldo et al. (1999), and Kim et al. (2000)). Thus, the question arises; is recombination spin dependent (Tandon et al. (2003)) or are singlet excitons generated in secondary processes? Direct measurement of the singlet generation rate in working devices of 44% has been shown (Rothe et al. (2006)), which have been verified as being part due to direct singlets formed on recombination and part from triplet fusion, singlets produced during triplet annihilation (Kondakov et al. (2009), King et al. (2011), and Zhang and Forrest (2012)). Here, the various routes by which triplet excitons can generate singlet states are discussed and their relative contributions to the overall electroluminescence yield are given. The materials requirements to obtain maximum singlet production from triplet states are discussed. These triplet contributions can give very high device yields for fluorescent emitters, which in the case of blue devices can be highly advantageous. Further, new devices architectures open up which are simple and have intrinsically low turn on voltages, ideal for large-area OLED lighting applications.

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