Evaluating first-principles electron–phonon couplings: consistency across methods and implementations

Abstract Electron–phonon coupling (EPC) is fundamental for understanding the behavior of molecules and crystals, influencing phenomena such as charge transport, energy transfer, phase transitions, and polaron formation. Accurate computational methods to calculate EPCs from first principles are essential, but their complexity has resulted in a variety of computational strategies, raising concerns about their mutual consistency. In this study, we provide a systematic benchmark of methods for EPC calculation by comparing two fundamentally different ab initio methodologies. We investigate Gaussian-type orbital methods based on the CP2K code and plane-wave-based projector-augmented-wave methods combined with maximally localized Wannier functions, as implemented in VASP and wannier90 . In addition, we further distinguish between the derivative–of–Hamiltonian ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> ) and derivative–of–states ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> ) approaches for obtaining EPC parameters. The comparison is conducted on a representative set of organic molecules, including pyrazine, pyridine, bithiophene, and quarterthiophene, varying significantly in size and flexibility. We find excellent agreement across implementations and basis sets when employing the same computational approach ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> ), demonstrating robust consistency between the numerical schemes. However, noticeable deviations occur when comparing the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> approaches within each code and for specific cases discussed in detail. Our findings emphasize the reliability of EPC computations using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> method and caution against potential pitfalls associated with the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> approach, providing guidance for future EPC calculations and model parameterizations.