Foundations of Chemistry 24 (1):73-86 (2022)

This manuscript explores the orthogonality constraints on configurations and orbitals subject to the property that states are mutually orthogonal. The orthogonality constraints lead to properties that affect the description of chemical systems. When states are described as linear combinations of configurations, the coefficient matrix diagonalises S−1H. Therefore, single-configuration states are only possible in one-electron systems: non-orthogonal configurations yield single-configuration states only if S−1H is diagonal, but this would violate the orthonormalisation constraint. Further, the coefficient matrix is not constrained to be square. Similarly, the orbitals used to construct configurations may also be orthogonal or non-orthogonal; orbitals are only required to be mutually orthogonal at the one-electron limit. Orthogonal orbitals are generally preferred due to their mathematical and conceptual simplicity, leading to fictitious unoccupied orbitals. Since the Fock operator is orthogonality agnostic, non-orthogonal orbitals can be generated by solving the Fock equation independently for each electron; the virtual orbitals produced by this conception are true excitation orbitals as they are eigensolutions of the Fock operator. Additionally, we show that the number of molecular orbitals generated is not restricted to the number of atomic orbitals employed in the computation. This manuscript explores the mathematical relationships that need to be satisfied under the various orthogonality regimes. We also present mathematical relationships that provide results that are independent of the orthogonality approximation within a particular computational method.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s10698-022-09417-y
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,316
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

First-Order Theories of Orthogonality Structures.Ruaan Kellerman - 2007 - Logic Journal of the IGPL 15 (3):255-270.
On the Modal Logic of the Non-Orthogonality Relation Between Quantum States.Shengyang Zhong - 2018 - Journal of Logic, Language and Information 27 (2):157-173.
Arithmetic Tools for Quantum Logic.J. C. Dacey - 1990 - Foundations of Physics 20 (5):605-619.
Are Orbitals Observable?Peter Mulder - 2011 - Hyle 17 (1):24 - 35.
Have Orbitals Really Been Observed?Eric R. Scerri - 2000 - Journal of Chemical Education 77:1492-1494.
The Recently Claimed Observation of Atomic Orbitals and Some Related Philosophical Issues.Eric R. Scerri - 2001 - Proceedings of the Philosophy of Science Association 2001 (3):S76-.
Why Orbitals Do Not Exist?Martín Labarca & Olimpia Lombardi - 2010 - Foundations of Chemistry 12 (2):149-157.
The Characteristic Sequence of a First-Order Formula.M. E. Malliaris - 2010 - Journal of Symbolic Logic 75 (4):1415-1440.


Added to PP index

Total views
5 ( #1,207,712 of 2,519,499 )

Recent downloads (6 months)
5 ( #137,544 of 2,519,499 )

How can I increase my downloads?


My notes