Abstract: Molecular design is often formulated as an optimization problem over existing molecular spaces. However, molecular optimization and the discovery of structurally distinct replacement molecules represent two fundamentally different search problems. LLM-based molecular design agents typically perform the former, conducting local refinement within the neighborhood of existing structures to improve target properties through structural modifications. In contrast, the latter requires exploration of a broader chemical space to discover molecules with entirely different scaffolds while preserving the functional characteristics of reference molecules. We propose MolHop, an agentic framework for cross-scaffold molecular discovery that enables models to navigate and edit within a pre-organized chemical space. MolHop organizes approximately 1.6 million molecular scaffolds from commercial molecules into a coarse-to-fine hierarchical action space. The agent selects new exploration regions through scaffold navigation actions and adjusts candidate properties through molecular editing. The framework maintains historical trajectory memory to support long-horizon search processes. On drug molecule and commercial compound tasks, connecting Grok-4.6 and DeepSeek-Flash-V4.1 to the MolHop framework substantially improves their cross-scaffold joint success rates. We develop MolHop-9B through agentic reinforcement learning, and MolHop-9B outperforms generative baselines including GPT-5.6-sol, Claude-5-Opus, and Gemini-3.1-Pro, while generating candidate molecules with larger scaffold differences from the reference molecules. These results demonstrate that effective molecular discovery beyond the traditional optimization paradigm requires structured chemical and action spaces, enabling agents to explore new structural regions rather than merely refine existing molecules.