Leveraging large language models (LLMs) for molecular generation has shown remarkable potential in chemical and drug design. Current methods primarily rely on supervised training or fine-tuning with limited datasets, which are insufficient to capture complex molecular design objectives. While some approaches attempt to guide generation toward specific goals, they often lack direct optimization mechanisms, making it difficult to align generated molecules with desired properties. To tackle these challenges, we propose \textbf{LLMol}, a principled reinforcement learning framework that directly incorporates verifiable rewards for targeted molecule generation. The key insight is to formulate molecular design as a goal-conditioned sequence prediction task, where verifiable rewards serve as explicit supervision to drive generation toward desired objectives. LLMol follows a two-stage training paradigm combining supervised learning and reinforcement learning. In the first stage, large language models are supervised fine-tuned to capture chemical syntax and molecular distributions. In the second stage, we introduce Reinforcement Learning with Verifiable Rewards (RLVR), which directly integrates property-based reward signals to guide molecular generation toward task-specific objectives. To address the high variance and instability common in discrete sequence optimization, we adopt Group Relative Policy Optimization (GRPO), a stable on-policy algorithm that smooths reward signals and improves training robustness. This framework enables LLMol to effectively handle a range of molecular design tasks, including single-property targeting (e.g., penalized logP, QED) and structure-constrained optimization. Experimental results demonstrate that LLMol consistently outperforms existing methods, achieving higher success rates and improved efficiency across diverse molecular benchmarks.

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