[Paper Review] Spectrum of extended systems from Reduced Density Matrix Functional Theory

S. Sharma, S. Shallcross+2 more|arXiv (Cornell University)|Dec 6, 2009

Advanced Physical and Chemical Molecular Interactions3 citations

TL;DR

This paper presents a method to calculate photoemission spectra in extended solids using Reduced Density Matrix Functional Theory (RDMFT), enabling accurate description of electronic gaps and orbital ordering in transition metal oxides. By deriving spectral functions from the energy derivative with respect to occupation numbers, the approach captures both Mott-Hubbard and charge-transfer physics, yielding excellent agreement with experiment and established many-body methods like GW and DMFT.

ABSTRACT

We present a method for calculating the spectrum of extended solids within reduced density matrix functional theory. An application of this method to the strongly correlated transition metal oxide series demonstrates that (i) an insulating state is found in the absence of magnetic order and, in addition, (ii) the interplay between the change transfer and Mott-Hubbard correlation is correctly described. In this respect we find that while NiO has a strong charge transfer character to the electronic gap, with substantial hybridization between $t_{2g}$ and oxygen-$p$ states in the lower Hubbard band, for MnO this is almost entirely absent. As a validation of our method we also calculate the spectra for a variety of weakly correlated materials, finding good agreement with experiment and other techniques.

Motivation & Objective

• To develop a spectral calculation method within RDMFT, a ground-state theory lacking spectral access.
• To address the failure of standard DFT to predict insulating states in transition metal monoxides (TMOs) even without magnetic order.
• To describe the interplay between Mott-Hubbard correlation and charge-transfer effects in TMOs, particularly in NiO, MnO, CoO, and FeO.
• To validate the spectral method against experimental XPS/BIS data and established ab-initio techniques like GW and DMFT.
• To demonstrate that RDMFT can correctly describe both the insulating gap and the detailed orbital ordering of $t_{2g}$ and $e_g$ states in TMOs.

Proposed method

• The method derives the spectral density function from the derivative of the total energy with respect to the occupation number of natural orbitals in RDMFT.
• It uses the one-body reduced density matrix (1-RDM) as the fundamental variable, diagonalized to obtain natural orbitals and occupation numbers.
• The Green's function is expressed in the natural orbital basis, and the imaginary part yields the spectral function $A_{\alpha\beta}(\omega)$, representing the spectral weight.
• The exchange-correlation energy is approximated using a power functional with $\alpha = 0.656$, ensuring $N$-representability and physical occupation numbers.
• The method is extended to the magnetic case by treating natural orbitals as spinors, allowing treatment of antiferromagnetic order.
• Spectral results are compared with XPS, BIS, GW, and DMFT data to validate accuracy and resolution of fine orbital features.

Experimental results

Research questions

• RQ1 Can RDMFT, a ground-state theory, be extended to yield reliable spectral functions for strongly correlated solids?
• RQ2 How accurately does the RDMFT spectral method describe the electronic gap in transition metal monoxides, particularly in the absence of long-range magnetic order?
• RQ3 To what extent does the method capture the subtle energy ordering between $t_{2g}$ and $e_g$ states in TMOs compared to GW and DMFT?
• RQ4 How does the inclusion of antiferromagnetic order affect the spectral predictions and band gaps in NiO, CoO, FeO, and MnO?
• RQ5 What is the relative contribution of Mott-Hubbard versus charge-transfer physics to the insulating gap in NiO vs. MnO?

Key findings

• The RDMFT spectral method correctly predicts an insulating ground state in TMOs even without magnetic order, resolving a key failure of standard DFT.
• For NiO, the method reveals significant hybridization between $t_{2g}$ and oxygen-$p$ states in the lower Hubbard band, indicating strong charge-transfer character.
• For MnO, such hybridization is nearly absent, indicating the insulating gap is primarily driven by Mott-Hubbard correlation.
• The calculated band gaps increase to 4.5 eV (experimental: 4.3 eV) for NiO and 2.6 eV (2.8 eV) for CoO when long-range antiferromagnetic order is included, improving agreement with experiment.
• The method reproduces the correct local magnetic moments: 1.36 $\mu_B$ (1.9 $\mu_B$ exp.) for NiO, 2.7 $\mu_B$ (3.3 $\mu_B$ exp.) for CoO, 3.35 $\mu_B$ (3.32 $\mu_B$ exp.) for FeO, and 3.38 $\mu_B$ (4.7 $\mu_B$ exp.) for MnO.
• The angular momentum-projected density of states shows excellent agreement with GW and DMFT, confirming accurate description of $t_{2g}$ and $e_g$ energy ordering and hybridization features.