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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.