الرَّحْمَانِ

A word in the Arabic language will either be 1) a verb or 2) a noun or 3) a particle – الرَّحْمَانِ is a noun

A noun may either be 1) Definite or indefinite 2) Masculine or feminine 3) Singular, dual or plural 4) Nominative, accusative or genitive

الرَّحْمَانُ is the natural state of this definite noun and it changes to الرَّحْمَانِ due to: 1) a preposition that precedes it or 2) a possessed noun that precedes it or 3) it’s a noun of dependent declension a) نَعْتٌ / صِفَطٌ adjectives b) التَّوْكِيْدُ emphatic c) المَعْطُوْفٌ conjunction d) البَدَلُ synonym

the inherent and inseparable quality of love, mercy and grace which comprehends the entire universe without regard to our effort and asking

even before we are born, pertaining to this life, manifested in the creation,

to love, have tenderness, mercy, pity, forgiveness, show goodness, favor, have all that is required to exercise beneficence

Grammatical analysis of الرَّحْمَانِ
اسْمٌ مَجْرُوْرٌ بِالكَسْرَةِ الزَّاهِرَةِ
مَعْرِفَةٌمُفْرَدٌمُذَكَّرٌمَجْرُوْرٌر ح مبَاب سَمِعَفَعْلَانُرَحِمَ يَرْحَمُاسْمٌ الصِّفَاتُ المُشَبَّهَةُ بِأَسْمَاءِ الْفَاعِلِ 
DefiniteSingularMasculineGenitiveRootMost MercifulPatternسNounAdjectives resembling participles
     Most Gracious   
      Most Loving   Grammatical analysis of الرَّحْمَانِ
Inherently Lovingاسْمٌ مَجْرُوْرٌ بِالكَسْرَةِ الزَّاهِرَةِ
Surah/Below are, the 11 verses in the holy Quran containing the genitive, definite, adjective, resembling an active participleالرَّحْمَانِ
Verse
  
1-1In the name of Allah, Most Compassionate, Eternally Mercifulبِسْمِ اللهِ الرَّحْمَانِ الرَّحِيْمِ
1-3Most Compassionate, Eternally Mercifulالرَّحْمَانِ الرَّحِيْمِ
those were whom Allah (SWT) bestowed favor upon them, from among the prophets of the offspringأُوْلَآئِكَ الَّذِيْنَ أَنْعَمَ اللهُ عَلَيْهِم مِّنَ النَّبِيِّينَ مِن ذُرِّيَّةِ 
of Adam (AS) and from whom We carried with Nuh (AS) and from the offspring of Ebrahim (AS)ءَادَمَ وَمِمَّنْ حَمَلْنَا مَعَ نُوحٍ وَمِن ذُرِّيَّةِ إِبْرَاهِيْمَ 
and Israel and from whom We guided, and We chose, when were recited to themوَإِسْرَآئِيْلَ وَمِمَّن هَدَيْنَا وَاجْتَبَيْنَآ إِذَا تُتْلَى عَلَيْهِم 
19-58the verses of the Most Compassionate, they fell, prostrating and weepingءَايَاتُ الرَّحْمَانِ خَرُّوا سُجَّدًا وَبُكِيًّا 
20-5 
20-90 
21-112 
25-59 
25-63 
27-30 
43-19 
43-36 
114-0In the name of Allah, Most Compassionate, Eternally Mercifulبِسْمِ اللهِ الرَّحْمَانِ الرَّحِيْمِ