Abstract
The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity—the electron density—without resorting to multi-electron wave functions. The inverse DFT problem of mapping the ground-state density to its exchange-correlation potential is instrumental in aiding functional development in DFT. However, the lack of an accurate and systematically convergent approach has left the problem unresolved, heretofore. This work presents a numerically robust and accurate scheme to evaluate the exact exchange-correlation potentials from correlated ab-initio densities. We cast the inverse DFT problem as a constrained optimization problem and employ a finite-element basis—a systematically convergent and complete basis—to discretize the problem. We demonstrate the accuracy and efficacy of our approach for both weakly and strongly correlated molecular systems, including up to 58 electrons, showing relevance to realistic polyatomic molecules.
Highlights
The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity—the electron density—without resorting to multi-electron wave functions
Vxc is a unique functional of the electron density, so there exists a one-to-one relationship from vxcðrÞ to ρðrÞ and vice versa
Recent efforts[21,22,23] have presented a different approach, which utilizes the two-electron reduced density matrix to remedy the non-uniqueness and the spurious oscillations in the obtained vxcðrÞ. This does not represent the solution of the inverse DFT problem, is not guaranteed to yield i.e., the the vxc input obtained from this electron density[23]
Summary
The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity—the electron density—without resorting to multi-electron wave functions. Given the large importance of this problem, there have been several attempts to solve the inverse DFT problem, employing either iterative updates[10,11,14,15,16] or constrained optimization approaches[9,12,17,18] These approaches have suffered from ill-conditioning, thereby resulting in non-unique solutions or causing spurious oscillations in the resultant vxcðrÞ. Recent efforts[21,22,23] have presented a different approach, which utilizes the two-electron reduced density matrix to remedy the non-uniqueness and the spurious oscillations in the obtained vxcðrÞ This does not represent the solution of the inverse DFT problem, is not guaranteed to yield i.e., the the vxc input obtained from this electron density[23]. The xc energy (Exc1⁄2ρ) can be directly evaluated through line integration on vxc1⁄2ρ
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
