I came across a couple of websites that have all the benefits of reciting certain names of Allah. For example, on the following two websites, it says that if you recite Ar-Rahmaan 100 times after each obligatory prayer, you will have good memory, a keen awareness, & be free of a heavy heart. And, if you recite Al Quddus 100 times each day, you will be free from anxiety. But there is no reference to any Hadiths or where they got these numbers or benefits from.

http://islamicpath.org/dua_names.html and http://www.wonderfulinfo.com/islam/the_names_of_allah/

Not only these two websites but a number of websites & dua books say the same thing. Are there any authentic Hadiths to support these or are they innovations that the Prophet (PBUH) never mentioned?

All praise be to Allah, and may His blessings and peace be on His last messenger, Muhammad,

They must have gotten those assertions from scholarly opinions. There is no hadeeth that indicates any of the above. The mention of the names of Allah in the appropriate supplications reported from the Messenger of Allah will bring about enormous benefits. You should also call upon Him by His most beautiful names. You may say O Rahman (Merciful) bestow your mercy on me, etc.

Although you may try scholarly anecdotes, you should not believe with confidence in the virtue of a certain modality, place, time, number of repetitions unless it is the Messenger of Allah who informed us of that virtue.

Here are some great du’a’s of the Prophet (sallAllahu ‘alaihi wa sallam) using Allah’s names; he said,

“Allah will relieve any slave who is afflicted with grief and anxiety from his anxiety and replace his grief with happiness if he says:

“اللهم اني عبدك وابن عبدك ابن أمتك ناصيتي بيدك ماض فيّ حكمك عدل فيّ قضاؤك أسألك بكل اسم هو لك سمّيت به نفسك أو أنزلته في كتابك أو علّمته أحدا من خلقك أو استأثرت به علم الغيب عندك أن تجعل القرآن ربيع قلبي ونور صدري وجلاء حزني وذهاب همّي”

‘O Allah! I am Your servant, son of Your servant, son of Your maidservant, my forelock is in Your hand, Your command over me is forever executed and Your decree over me is just. I ask You by every name belonging to You which You named Yourself with, or revealed in Your Book, or You taught to any of Your creation, or You have preserved in the knowledge of the unseen with You, that You make the Qur’aan the life of my heart and the light of my chest, and a departure for my sorrow and a release for my anxiety. O Allah! Teach me from it that which I am ignorant of and remind me with it that which I was made to forget; I ask You by Your mercy, for You are the Most Merciful, to grant me its recitation during the hours of night and day in the form which pleases You’” . The people asked: “O Prophet of Allah! Should we learn (i.e., memorize) these words’. He sallAllahu ‘alaihi wa sallam replied: “Yes! Everyone who hears this should memorize it”.

Muslim reported from Ibn ‘Abbas that the Messenger of Allah used to say the following during times of distress:

“لَا إِلَهَ إِلَّا اللَّهُ الْعَظِيمُ الْحَلِيمُ ، لَا إِلَهَ إِلَّا اللَّهُ رَبُّ الْعَرْشِ الْعَظِيمِ ، لَا إِلَهَ إِلَّا اللَّهُ رَبُّ السَّمَاوَاتِ وَرَبُّ الْأَرْضِ وَرَبُّ الْعَرْشِ الْكَرِيمِ”.

“There is no god except Allah, the All-Mighty, the Forbearing; there is no god except Allah, the Lord of the Mighty Throne; there is no god except Allah, the Lord of the heavens, the Lord of the earth, and the Lord of the noble Throne.”

Allah knows best.