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hokhani
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Why the ground state HOMO level of a molecule with two opposite-spin electrons, is singlet while we know that a level with two opposite-spin electrons may be singlet(s=0,m=0) or triplet(s=1,m=0)?
DrDu said:The total wavefunction has to be antisymmetric. For two electrons in one orbital ##\phi## the Slater determinant can be written as
##\begin{vmatrix} \phi(1)s_+(1)& \phi(1) s_-(1)\\ \phi(2)s_+(2) &\phi(2) s_-(2) \end{vmatrix}= N\phi(1)\phi(2)(s_+(1)s_-(2)-s_-(1)s_+(2))##
where N is a normalization constant and s_+ and s_- are up or down spin eigenfunctions.
So as the orbital part of the wavefunction can only be symmetric, the spin function has to be antisymmetric.
With two orbital functions, you can form two Slater determinants and also create triplet eigenfunctions, e.g.
##N(\phi_a(1)\phi_b(2)-\phi_b(1)\phi_a(2))(s_+(1)s_-(2)+s_-(1)s_+(2))##
Excuse me. I didn't underestand what you mean by "with two orbitals you can form two different Slater determinants". Do you mean thatDrDu said:As I said with two orbitals you can form two different Slater determinants. The wavefunction with definite spins I have written down are combinations of the two.
The second one being
##
\begin{vmatrix} \phi_a(1)s_-(1)& \phi_b(1) s_+(1)\\ \phi_a(2)s_-(2) &\phi_b(2) s_+(2) \end{vmatrix}
##
The ground state of a molecular material refers to its lowest energy state, in which the molecules are arranged in their most stable configuration.
The ground state of a molecular material is determined through various methods, including theoretical calculations, spectroscopic techniques, and X-ray crystallography.
The ground state of a molecular material is influenced by factors such as the composition and arrangement of its atoms, the strength of chemical bonds, and external factors such as temperature and pressure.
Yes, the ground state of a molecular material can change if there is a change in the conditions or environment in which it exists. For example, an increase in temperature or exposure to radiation can cause the molecules to transition to a higher energy state.
Studying the ground state of a molecular material can provide valuable insights into its physical and chemical properties, as well as its potential applications in fields such as materials science, nanotechnology, and drug discovery.