Discussion Overview
The discussion centers on the validity of the virial theorem within the Hartree Fock approximation, exploring theoretical underpinnings and references to literature on the topic. Participants seek to understand why the theorem applies in this context and inquire about resources for further reading.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- One participant questions the validity of the virial theorem in the Hartree Fock approximation and notes that some authors mention it without explanation.
- Another participant references Werner Kutzelnigg's books as a source that discusses the topic in detail, although they are in German.
- A participant expresses a lack of access to Kutzelnigg's books and requests online resources for the derivation of the theorem.
- It is suggested that derivations may be found in older quantum chemistry textbooks, particularly from the 1970s and earlier.
- A participant mentions that Vladimir Fock's original works contain the derivation of the theorem, specifically in a 1930 paper, and provides a link to a translation.
- There is a note that the derivation explains the theorem's validity for variational solutions to the Schrödinger equation, but additional work is needed to understand its application in the Hartree Fock approximation.
- Another participant points out that while the virial theorem holds for Hartree Fock, it may not hold for Linear Combination of Atomic Orbitals (LCAO) without scaling the atomic orbitals, which is often overlooked in calculations.
- It is mentioned that the latest edition of Kutzelnigg's books is from 2003, indicating that they are not outdated.
Areas of Agreement / Disagreement
Participants express differing views on the applicability of the virial theorem in various contexts, particularly between Hartree Fock and LCAO methods. The discussion remains unresolved regarding the specifics of the theorem's validity in these frameworks.
Contextual Notes
Some participants note the potential difficulty in finding accessible resources and the reliance on older literature for derivations. There is also an acknowledgment of the need for further work to clarify the theorem's application specifically to the Hartree Fock approximation.