The Collaborative International Dictionary of English v.0.48:

Intentness \In*tent"ness\, n.
   The state or quality of being intent; close application;
   attention.
   [1913 Webster]

         Extreme solicitude or intentness upon business.
                                                  --South.
   [1913 Webster]

WordNet (r) 3.0 (2006):

intentness
    n 1: the quality of being intent and concentrated; "the
         intentness of his gaze" [syn: intentness, engrossment]

Moby Thesaurus II by Grady Ward, 1.0:

81 Moby Thesaurus words for "intentness":
   abandon, absorbed attention, absorption, advertence, advertency,
   alertness, application, ardency, ardor, assiduity, assiduousness,
   attention, attention span, attentiveness, awareness, care,
   commitment, committedness, concentration, consciousness,
   consideration, contemplation, dedication, deep study, deep thought,
   devotedness, devotion, devoutness, diligence, ear, earnest,
   earnestness, engagement, engrossment, faith, faithfulness,
   fervency, fervidness, fervor, fidelity, fire, heartiness, heat,
   heatedness, heed, heedfulness, immersion, impassionedness,
   intensity, intentiveness, involvement, loyalty, meditation,
   mindfulness, monomania, note, notice, observance, observation,
   obsession, passion, passionateness, preoccupation,
   profound thought, rapt attention, regard, regardfulness, remark,
   resolution, respect, seriousness, sincerity, single-mindedness,
   spirit, studiousness, study, submersion, thought, vehemence,
   warmth, zeal