How can a woman atone for the sin of adultery committed after she became aware of her husband's adultery and his neglect of her?

You must offer sincere and truthful repentance and regret what you have done, and increase in charity and good deeds that expiate sins, such as Hajj. In addition, you must adhere to prayer, the hijab (definition), avoid ostentatious display, stay away from places of temptation and bad female company, and avoid mingling with men, while keeping company with righteous women and focusing on household affairs and raising children. For Allah accepts repentance and forgives all sins.