Two user Gaussian interference channel (GIC) consists of two source-destination pairs which transmit independent messages and interfere with each other. The best achievable rate region, referred to HK sum rate bound, requires the sources to split the information into public messages and private messages. As Gaussian signaling holds the potential of approaching the capacity, finding the HK sum rate achieved by Gaussian signaling is of great importance. However, The optimal power allocation over messages for Gaussian signaling are not known yet This work clearly describes the optimal power allocation and corresponding sum rate achieved by Gaussian signaling without time sharing (TS) in closed form. It lays a foundation for finding the TS strategy achieving the optimal sum rate. The obtained power allocation indicates that without TS, message splitting may not be always necessary. Besides, the conditions for using and not using message splitting are also characterized in detail.