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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 117, 2019 - Issue 17: 58th Sanibel Symposium Proceedings
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58th Sanibel Symposium

A comparison of the scalar Hermitian product versus the complex product for obtaining electron densities and Fukui functions from complex wavefunctions for the temporary anion resonance states of Be, Mg and Ca

Pages 2195-2200 | Received 06 Mar 2018, Accepted 07 Jun 2018, Published online: 24 Jun 2018
 

ABSTRACT

Densities and Fukui functions using the complex product, c-product (f|g) and the scalar Hermitian product <f|g> are compared for two 2P resonance states of Be, the 2P resonance state of Mg and the 2D resonance state of Ca. Use of the c-product has been shown to be necessary when analysing the complex eigenfunctions of a complex-scaled Hamiltonian. The c-product produces complex electron densities from complex wavefunctions, but only the real part is used for the Fukui functions. The real part of the density matrix obtained using the c-product doesn’t satisfy the Pauli principle, and can produce negative regions in the electron densities. The Fukui functions and densities obtained using the c-product compare well with the Fukui functions and densities obtained using the scalar Hermitian product.

GRAPHICAL ABSTRACT

4. Discussion

While the complex product has many desirable features when calculating properties and interpreting complex wavefunctions that are eigenfunctions of complex-scaled Hamiltonians, there are also cases where the scalar Hermitian product is useful. For example, the Pauli principle is satisfied for the real reduced density matrix when using the scalar Hermitian product, but not when using the complex product. Both densities integrate to N, the number of electrons. The two methods produce real densities and Fukui functions that differ only slightly, being nearly visually identical.

Acknowledgements

The author thanks the East Carolina University Center for Applied Computational Studies for computational resources. And thanks to Professor Carlos F. Bunge for the continuing use of his atomic CI programs ATMOL and AUTOCL.

Disclosure statement

No potential conflict of interest was reported by the author.

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