Low-order anharmonic contributions to the internal energy of the one-component plasma

We present precise calculations of the second-order cubic and first-order quartic anharmonic contributions to the internal energy of the one-component plasma (OCP), which are then used with available computer-simulation data to estimate the size of higher-order anharmonic effects. We show that in both the zero-temperature and high-temperature limits the OCP is very harmonic. At zero temperature, we find that the two lowest-order anharmonic contributions are the largest anharmonic contributions, and of the two the second-order cubic contribution is nearly three times the first-order quartic. At high temperatures, we find that the second-order cubic contribution is about twice that of the first-order quartic, but their combined contribution to the internal energy is small compared with our estimate of the next-order anharmonic terms.