A transformed coordinate approach to accurate and efficient solutions of many-electron Schrödinger equations for molecules

We extend our recently developed transformed-coordinate method for solving the Schrödinger equations of many-electron molecules. Each relative Cartesian coordinates in the original equation is independently mapped to a new coordinate system using a sign square-root transformation. The resulting Hamiltonian leads to a rapid decay of the wave function due to a reduction in kinetic energy and the scaling of potential energy with the square of the distance. Electron-nucleus interactions and electron correlation effects within the electron-electron repulsion term are accurately represented, leading to total energies and energy components that are consistent with accurate approaches. Furthermore, not only is the virial ratio in excellent agreement with its ideal value, but the resulting wave function also captures both radial and angular electron correlation. In addition, the transformed method significantly reduces computational cost, offering a favorable balance between accuracy and efficiency, and making it suitable for calculations of larger systems. • A transformed-coordinate approach for solving many-electron Schrödinger equations is developed and extended. • Independent sign square-root transformations of relative Cartesian coordinates yield a rapidly decaying wave function. • The transformed Hamiltonian accurately captures electron–nucleus interactions and electron–electron correlations. • Total energies, energy components, and virial ratios show excellent agreement with accurate reference methods. • The method substantially reduces computational cost while retaining high accuracy, enabling applications to larger systems.