The first-principles calculation of Bloch state derivatives is numerically challenging yet indispensable for evaluating the quantum response functions of materials. Here, we propose a band-resolved automatic differentiation (BRAD) approach for efficiently calculating quantum response properties, by developing a forward-mode automatic differentiation framework based on a modified Nelson's method. The BRAD approach offers two key advantages over existing methods: (i) The calculation is carried out in a band-by-band manner, removing the need for a time-consuming full-band summation. (ii) Bloch state derivatives can be computed to arbitrary orders through automatic differentiation, eliminating the need for manual analytical derivations and complex computational implementations. We demonstrate the reliability of our approach by computing the nonlinear optical responses of monolayer ${\mathrm{WS}}_2$ and further highlight its usefulness in studying high-order quantum response properties.

Close

PrevNext

View figure in article

• Electronic structure
• Nonlinear optics
• Photoconductivity
• 2-dimensional systems
• First-principles calculations