1) Frankly 2) Naively 3) Purely 4) Trustingly 1) In a dewy-eyed way 2) In a naively innocent manner 3) In a not unlawful manner 4) Not knowing any better 
• (adv.) In an innocent manner.
In'no·cent·ly adverb In an innocent manner. 
[adv] - in a not unlawful manner 2. [adv] - in a naively innocent manner
innocently 1. In a naively innocent manner; such as, the child smiled at her innocently. 2. Characterized by being free from guilt or sin especially through lack of knowledge of evil. 3. A reference to being blameless; harmless in effect or intention.
adverb in a naively innocent manner; `she smiled at him innocently`