Lewis & Short

dē-spēro, āvi, ātum, 1, v. n. and a., to be hopeless; to have no hope of, to despair of, to give up (freq. and class.).
Constr. most freq. with de, the acc., or acc. and inf.; less freq. with the dat. or absol.

        1. (α) With de (in Cic. rarely): de sua virtute aut de ipsius diligentia, Caes. B. G. 1, 40, 4: de pugna, id. ib. 1, 40, 8: de officio imperatoris, id. ib. 1, 40, 10,: de expugnatione, id. ib. 7, 36: de salute, id. ib. 7, 85, 3: de republica, Cic. Att. 8, 11, D, § 6: de summa rerum, Liv. 26, 41: de se, Planc. ap. Cic. Fam. 10, 21, 3; Cic. Fam. 7, 3, 2; 9, 15, 5; Lact. 6, 24, 1; Sen. Tranq. An. 5, 2.
        2. (β) With acc. (in Caes. only in the part. perf.): honores, Cic. Cat. 2, 9: honorem, id. Mur. 21, 43: rempublicam, id. Fam. 12, 14, 3: pacem, id. Att. 8, 15, 3: voluntariam deditionem, Liv. 23, 14: membra invicti Glyconis, Hor. Ep. 1, 1, 30; Sen. Ep. 29, 3; 104, 12.
          In the pass.: sive restituimur, sive desperamur, Cic. Q. Fr. 1, 3, 7; Quint. 1, 10, 8: hujus salus desperanda est, Cic. Lael. 24, 90; cf.: nil desperandum Teucro duce, Hor. Od. 1, 7, 27: desperatis nostris rebus, Caes. B. G. 2, 24, 4; cf. id. ib. 3, 26, 5: desperata salute, id. ib. 3, 3, 3 et saep.: desperato improviso tumultu, Liv. 10, 14 et saep.
          Middle: desperatis hominibus, who gave themselves up, i. e. were desperately resolved, desperate, Caes. B. G. 7, 3.
        3. (γ) With acc. and inf.: ego non despero fore aliquem aliquando, qui, etc., Cic. de Or. 1, 21, 95; id. Div. 2, 21, 48; Quint. 5, 12, 3; Hor. A. P. 150; Ov. M. 9, 724 et saep.
        4. (δ) With dat.: saluti, Cic. Clu. 25, 68: oppido, id. Pis. 34 fin.: rebus tuis, id. ib. 36, 89: suis fortunis, Caes. B. G. 3, 12, 3: sibi, id. ib. 7, 50, 4; Cic. Mur. 21 fin.: saluti suae, id. Clu. 25.
          (ε) Absol.: sive habes aliquam spem de republica sive desperas, Cic. Fam. 2, 5; id. Off. 1, 21 fin.; Quint. 2, 4, 10; 12 prooem. § 2; Ov. M. 10, 371 et saep.: spem habere a tribuno plebis, a senatu desperasse, Cic. Pis. 6.
          Hence,
    1. * 1. dēspēranter, adv., hopelessly, despairingly: loqui secum, Cic. Att. 14, 18, 3.
    2. 2. dēspērātus, a, um, P. a., given up, despaired of, irremediable, desperate (most freq. in Cic.): exercitum collectum ex senibus desperatis, Cic. Cat. 2, 3: remedium aegrotae ac prope desperatae reipublicae, id. Div. in Caecil. 21, 70; cf.: reipublicae morbi, id. Sull. 27 fin.: collegium, id. Leg. 3, 10, 24: desperatas pecunias exigere, id. Mur. 20 fin. et saep.: desperatos vocant, quia corpori suo minime parcunt (of the Christians), Lact. 5, 9, 12.
      Prov.: desperatis Hippocrates vetat adhibere medicinam, Cic. Att. 16, 15, 5.
      Comp.: haec nunc multo desperatiora, Cic. Fam. 7, 22.
      Sup.: perfugium, Cic. Verr. 2, 2, 41 fin.: spes, Balb. ap. Cic. Att. 9, 7, B, § 2.
      * Adv., dēspērātē, desperately: non desperate sollicitus, Aug. Ep. ad Celer. 237.