Importance of intersite Hubbard interactions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mrow><mml:mi>MnO</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:math> : A first-principles <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>DFT</mml:mi><mml:mo>+</mml:mo><mml:mi>U</mml:mi><mml:mo>+</mml:mo><mml:mi>V</mml:mi></mml:mrow></mml:math> study

We present a first-principles investigation of the structural, electronic, and magnetic properties pyrolusite ($\beta$-MnO$_2$) using conventional extended Hubbard-corrected density-functional theory (DFT+$U$ DFT+$U$+$V$). The onsite $U$ intersite $V$ Hubbard parameters are computed linear-response in framework perturbation theory. show that while inclusion is crucial to describe localized nature Mn($3d$) states, key capture accurately strong hybridization between neighboring O($2p$) states. In this framework, we stabilize simplified collinear antiferromagnetic (AFM) ordering (suggested by Goodenough-Kanamori rule) commonly used as an approximation experimentally-observed noncollinear screw-type spiral ordering. A detailed ferromagnetic other three AFM spin configurations also presented. findings from DFT discussed two kinds manifolds - nonorthogonalized orthogonalized atomic orbitals showing special attention must be given choice projectors, with providing more accurate results than ones within DFT+$U$+$V$. This work paves way for future studies complex transition-metal compounds containing strongly electrons presence pronounced covalent interactions.