Symmetry Considerations in Hartree-Fock-Roothaan Method

In summary: A fellow quantum chemist/physicist.In summary, the conversation discusses the restricted closed-shell Hartree-Fock method, a simplified approach used in quantum chemistry. The question raised is whether or not to consider gerade and ungerade symmetries of the core Hamiltonian and two-electron integrals, as well as positive and negative parity, when implementing the method. The expert advises that these considerations are not necessary for the restricted closed-shell Hartree-Fock method, but it is always important to double check results and compare them to other methods or experimental data.
  • #1
twist.1995
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1
Hello, dear Quantum Chemists or Physicists.
I have been extensively researching the restricted closed-shell Hartree-Fock method, and wrote a code that is working for diatomic molecules, like H2 or He2++. I, however, have a few unresolved questions that do not allow me to proceed further in checking my results. Particularly, I am concerned whether or not I should consider gerade and ungerade symmetries of the core hamiltonian and two-electron integrals. Particularly, I am wondering whether I should consider positive and negative parity prior to implementing my code. I would extremely appreciate if anyone can answer to my question. Thanks.
 
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Thank you for your question regarding the restricted closed-shell Hartree-Fock method. As a scientist in the field, I would be happy to provide some insight and guidance.

Firstly, it is important to note that the restricted closed-shell Hartree-Fock method is a simplified approach that assumes all electrons in a molecule are paired and have opposite spin. This means that the wavefunction is symmetric with respect to particle exchange and has a definite parity (either even or odd). Therefore, it is not necessary to consider gerade and ungerade symmetries of the core Hamiltonian and two-electron integrals. These symmetries only need to be considered in more complex methods that allow for broken symmetry.

In terms of parity, it is also not necessary to consider positive and negative parity prior to implementing your code. This is because the restricted closed-shell Hartree-Fock method automatically takes into account the correct parity of the wavefunction.

However, it is always a good practice to double check your results and make sure they are consistent with what is expected. You can do this by comparing your results to those obtained from other methods or experimental data.

I hope this helps answer your questions. If you have any further concerns, please do not hesitate to ask. Keep up the good work with your research!
 

Related to Symmetry Considerations in Hartree-Fock-Roothaan Method

1. What is the Hartree-Fock-Roothaan method?

The Hartree-Fock-Roothaan method is a computational technique used in quantum chemistry to calculate the electronic structure of atoms and molecules. It is based on the Hartree-Fock approximation, which assumes that the electrons in a system behave independently of each other. The Roothaan equations are solved iteratively to determine the best set of molecular orbitals that describe the electronic structure of the system.

2. Why are symmetry considerations important in the Hartree-Fock-Roothaan method?

Symmetry considerations are important in the Hartree-Fock-Roothaan method because they can greatly simplify the calculations. By taking into account the symmetries of the system, the number of integrals that need to be computed can be reduced, making the calculations more efficient. Additionally, symmetry-adapted basis functions can be used, which can improve the accuracy of the results.

3. How are symmetry considerations applied in the Hartree-Fock-Roothaan method?

Symmetry considerations are applied in the Hartree-Fock-Roothaan method through the use of group theory. The symmetry of the system is determined and used to classify the molecular orbitals and integrals. This allows for the selection of the most appropriate set of basis functions and simplification of the Roothaan equations. Group theory also helps to identify degenerate orbitals, which have the same energy level, and can aid in predicting the electronic and spectroscopic properties of the system.

4. What are the benefits of using symmetry-adapted basis functions in the Hartree-Fock-Roothaan method?

Using symmetry-adapted basis functions in the Hartree-Fock-Roothaan method can improve the accuracy of the results. These basis functions are constructed to have the same symmetry as the molecular orbitals, which can reduce the number of variational parameters and improve the convergence of the calculations. Additionally, they can help to reduce the computational cost by eliminating redundant calculations.

5. Are there any limitations to using symmetry considerations in the Hartree-Fock-Roothaan method?

While symmetry considerations can greatly simplify the calculations in the Hartree-Fock-Roothaan method, there are some limitations. If the system does not have a high degree of symmetry, the benefits of using symmetry-adapted basis functions may be limited. Additionally, the use of symmetry can also lead to some loss of accuracy, as it can only approximate the true electronic structure of the system. Therefore, a balance must be struck between the simplification and accuracy of the calculations when applying symmetry considerations in this method.

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