Low Scaling Quantum Chemistry Methods for Predicting Electronic Properties of 2D Materials

The electronic structure of periodic systems, such as 2D materials, presents significant computational challenges due to the infinite nature of these systems. While density functional theory (DFT) has been the cornerstone for such calculations, it can sometimes fall short in accurately predicting properties like band gaps and Van der Waals interactions. Ab initio quantum chemistry methods, traditionally developed for molecular systems, offer a systematically improvable alternative. In particular, spin-component scaled (SCS) and scaled opposite-spin (SOS) modifications of second-order Møller-Plesset perturbation theory (MP2) have shown improved accuracy over conventional MP2 for molecular properties and hold potential for application to periodic systems.<br/>This work aims to extend and apply SCS and SOS MP2 methods to simulate and predict the electronic properties of complex 2D materials. These methods, known for their balance between computational cost and accuracy, have proven effective for molecular systems in predicting ground state properties. They have relatively low scaling and mostly give an accuracy that is better than MP2, and for some properties even can be comparable to CCSD. Their application to periodic systems, however, remains limited. Our research focuses on developing efficient algorithms for periodic SCS and SOS MP2 calculations using Gaussian type orbitals, Brillouin zone sampling, and density fitting techniques.<br/>We present a novel periodic SOS-MP2 algorithm based on density fitting and Laplace transformation, which reduces the computational scaling with respect to the number of basis functions and k-points. This approach leads to an attractive low-scaling approach for periodic systems<b> </b>with complex unit cells. Preliminary results show that periodic SCS/SOS-MP2 calculations provide accurate ground state properties. These methods outperform leading density functionals and offer a reliable approach to reaching the thermodynamic limit in extended systems.<br/>Our preliminary promising results demonstrate the potential of these methods for Van der Waals 2D materials. Since both Van der Waals 2D materials and point defects present significant challenges for density functional theory (DFT) methods, the application of a novel periodic SOS-MP2 algorithm can aid in the development of novel exchange-correlation functionals and force fields for molecular dynamics applications.<br/>Furthermore, accurately predicting and understanding electronic properties and transfer mechanisms in these systems could lead to the discovery of novel materials and phenomena. Significant implications are expected for device design and quantum information applications, since point defects in 2D materials, in particular, are promising candidates for quantum information technologies.<br/>In summary, this work introduces and applies advanced quantum chemistry methods to periodic systems, demonstrating their effectiveness and potential for broader application in material science and condensed matter physics. By extending the capabilities of SCS and SOS MP2 methods to complex 2D materials, we pave the way for more accurate and efficient computational techniques in the study of extended systems.