He divorced his wife on the basis of a false accusation
Question

                There was an argument between me and my wife, and I doubted her chastity and honour, so I divorced her for that reason. Then after that I realized that these accusations were false and had no basis in truth. Does this divorce count as such?.
Praise be to Allah.If you only divorced your 
    wife on this basis, then you realized that she was innocent of that, then 
    the divorce  does not count, because it was based on a reason, then it 
    became apparent that this reason had no substance. This is the view favoured 
    by Shaykh al-Islam Ibn Taymiyah and Ibn Rajab, and it has been stated in 
    fatwas issued by two contemporary shaykhs: Muhammad ibn Ibraaheem and Ibn 
    ‘Uthaymeen (may Allaah have mercy on them both) 

    Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) 
    said: 

    If it is said, “Your wife committed zina” or “She went out of 
    the house” and he gets angry and says, “Then she is divorced,” the divorce 
    does not count. This was stated in a fatwa by Ibn ‘Aqeel, and it is the view 
    of ‘Ata’ ibn Abi Rabaah. Something similar was said by Ibn Abi Moosa. If he 
    said to his wife, “You are divorced because you entered the house,” she is 
    not divorced if she did not enter the house, because he only divorced her 
    for a reason, without which the divorce does not take effect. End quote. 

    Al-Fataawa al-Kubra, 5/495 

    See: Qawaa’id Ibn Rajab al-Hanbali, p. 323 

    Shaykh Muhammad Ibraaheem (may Allaah have mercy on him) 
    said: 
We have received your 
    letter in which you are asking about your divorcing your wife, and you say 
    that your heard something about her so you got angry and divorced her three 
    times. After that you found out that the news was false, and it was proven 
    that it was not true, and you are asking whether this divorce counts as such 
    or not, because it turned out that she is innocent of what was being said 
    about her. 

    The answer:  
If the situation is as described, and 
    you only divorced her on the basis of that false news, then the correct 
    scholarly view is that the divorce does not count as such. Based on this, 
    the divorce is invalid and the woman is permissible for you under the 
    initial marriage contract, so there is no need for you to formally take her 
    back or do a new marriage contract. End quote. 
    
    Fataawa Muhamamd ibn Ibraaheem, 
    11/ question no. 3159 

    Shaykh Ibn ‘Uthaymeen said in al-Sharh al-Mumti’, 
    6/245 
If a person bases his words on a reason which 
    is later found to have no substance, there is no ruling on his words. This 
    is a basic principle which has many implications, among the most important 
    of which is what happens to some people with regard to divorce, where a man 
    says to his wife for example, “If you enter the house of So and so then you 
    are divorced,” based on what that person has of haraam means of 
    entertainment such as musical instruments and the like, then he finds out 
    that he has no such things at all. If she enters that house, is she divorced 
    or not? The answer is that she is not divorced, because that was based on a 
    reason which has no substance. This is based on both sharee’ah and rational 
    thinking. End quote.