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Rainbows_
What are the different eigenstates of molecules that are most often used in chemistry?
blue_leaf77 said:What do you mean by different eigenstates of molecules? There is only one set of eigenstates of (the Hamiltonian of) a given molecule.
HAYAO said:Unfortunately, the question does not make sense.
I am guessing that OP do not understand the concept of eigenstates, eigenvalues, and what it means for a molecule to have them under the Hamiltonian.
"Energy eigenstates" does not make sense. Eigenvalues of a Hamiltonian of a given molecule are the energies. Each of these energies corresponds to each of the eigenstates of a Hamiltonian of a given molecule.
HAYAO said:Unfortunately, the question does not make sense.
I am guessing that OP do not understand the concept of eigenstates, eigenvalues, and what it means for a molecule to have them under the Hamiltonian.
"Energy eigenstates" does not make sense. Eigenvalues of a Hamiltonian of a given molecule are the energies. Each of these energies corresponds to each of the eigenstates of a Hamiltonian of a given molecule.
Rainbows_ said:What I wanted to know are examples of energy eigenstates of the molecules. If I hit them with laser, what are the possible quantized energy eigenstates (or eigenstates of the Hamiltonian)?
Sometimes, the Hamiltonian operator is also referred to as the energy operator. Thus its eigenvalues are called energy eigenstates in this sense.HAYAO said:Perhaps people call it "energy eigenstates" for convenience or it's a real term and has been given a definition, despite the possible confusion to the readers if they were taken literally.
Your question still seems vague to me, by examples do you mean you want a graphical example? If you do some computational chemistry calculation you will know that two eigenstates differing in only one level of energy can have a significantly different shape that giving only a particular example does not seem meaningful, at least to me. Anyway, it might be possible to find such graphical representation of a particular state of a particular molecule in scientific papers. Just need to warn you that due to the many-body nature of molecules you might not get a complete coordinate dependency of these states.Rainbows_ said:What I wanted to know are examples of energy eigenstates of the molecules. If I hit them with laser, what are the possible quantized energy eigenstates (or eigenstates of the Hamiltonian)?
You probably meant eigenstates, not eigenvalues.blue_leaf77 said:Sometimes, the Hamiltonian operator is also referred to as the energy operator. Thus its eigenvalues are called energy eigenstates in this sense.
kith said:You probably meant eigenstates, not eigenvalues.
Eigenstates of molecules refer to the quantum mechanical states that describe the energy and spatial distribution of electrons within a molecule. These states are determined by the molecule's Hamiltonian operator and can be thought of as the "allowed" energy levels for electrons within the molecule.
The calculation of eigenstates of molecules involves using quantum mechanical methods such as the Schrödinger equation. This equation takes into account the potential energy of the molecule and solves for the wavefunction, which describes the probability of finding an electron at a certain energy level.
Eigenstates of molecules are important in chemistry because they determine the electronic structure and properties of molecules. The energy levels and spatial distribution of electrons play a crucial role in bonding, reactivity, and other chemical processes.
Yes, molecules can have multiple eigenstates. In fact, most molecules have multiple energy levels and corresponding eigenstates. This allows for a variety of possible electronic configurations and behaviors.
Eigenstates of molecules play a key role in spectroscopy, which is the study of how molecules interact with electromagnetic radiation. The energy differences between eigenstates can be observed through the absorption or emission of specific wavelengths of light, providing valuable information about molecular structure and properties.