Multicomponent Coupled Cluster Singles and Doubles with Density Fitting: Protonated Water Tetramers with Quantized Protons

Nuclear quantum effects such as zero-point energy are important for describing a wide range of chemical properties. The nuclear-electronic orbital (NEO) approach incorporates such effects into quantum chemistry calculations by treating specified nuclei, typically protons, quantum mechanically on the same level as electrons. Herein, both the traditional and t1-transformed NEO coupled cluster with singles and doubles (NEO-CCSD) methods are implemented with a density fitting (DF) scheme for approximating the four-center two-particle integrals. The enhanced computational efficiency enables calculations on larger molecules with multiple quantum protons. The NEO-DF-CCSD method predicts proton affinities within chemical accuracy. Its application to protonated water tetramers with all nine protons treated quantum mechanically produces the qualitatively correct ordering of the isomer energies, which are strongly influenced by the zero-point energy contributions inherently included in NEO energy calculations. This work showcases the capabilities of the NEO-DF-CCSD method and provides the foundation for future developments and applications.