Monogenes and the Hebrew Bible
We turn now to consider the usage of μονογενής in the LXX, its relation to the Hebrew word yachid (יָחִיד), and the reverse relation of yachid to ἀγαπητός. The LXX has ten occurrences of μονογενής. One is a post-LXX Christian text and can be set aside for now.
Judges 11:34 depicts the Jephthah’s return home in light of his ominous oath in vv30-31. The text intentionally highlights that he has only one child:
καὶ αὕτη μονογενὴς αὐτῷ ἀγαπητή, καὶ οὐκ ἔστιν αὐτῷ πλὴν αὐτῆς υἱὸς ἢ θυγάτηρ. And she was his beloved, only child, and he had no son or daughter apart from her.
The relevant Hebrew text combines both the adverb raq and the key term yachid, which may explain the double-translation of μονογενής and ἀγαπητή.
ווְרַק֙ הִ֣יא יְחִידָ֔ה אֵֽין־ל֥וֹ מִמֶּ֛נּוּ בֵּ֖ן אֹו־בַֽת׃
The repetition, and then the somewhat redundant clarification that there is no other son nor daughter, is designed to heighten the pathos of the situation. It also instances yachid as the most common translation basis for μονογενής in the LXX.
The story of Tobit strengthens the case that μονογενής refers primarily to a siblingless child, since this is part of the emotional impact of the story. The term appears three times, in 3:15 in Sarra’s prayer as she laments that although she is her father’s only child, his line will expire without an heir. Of note, she also uses μία to describe herself in 3:10. She is again described as a μονογενής in 6:11. The term then appears once more in 8:17, this time in the plural μονογενεῖς, as Ragouel praises God for having mercy on these two only-children. The usage is consistent throughout this text.
Psalms of David
There are three occurrences in the Psalms. The first is relatively straightforward, in that μονογενής occurs with πτωχός, and is part of a depiction of being alone and in a desperate condition. Whether yachid is properly translated here is besides our main point, the translation has understood it as ‘alone’ in the context of familial relations.
24:16 (25:16) ἐπίβλεψον ἐπʼ ἐμὲ καὶ ἐλέησόν με,
ὅτι μονογενὴς καὶ πτωχός εἰμι ἐγώ.
Look upon me and have mercy on me,
because I am an only child and poor.
The two other uses are more difficult, in that μονογενής appears to have undergone some extension of meaning.
21:21 (22:21) ῥῦσαι ἀπὸ ῥομφαίας τὴν ψυχήν μου
καὶ ἐκ χειρὸς κυνὸς τὴν μονογενῆ μου
Save my life from the sword,
and my monogenēs from the hand of the dog.
34:17 (35:17) κύριε, πότε ἐπόψῃ;
ἀποκατάστησον τὴν ψυχήν μου ἀπὸ τῆς κακουργίας αὐτῶν,
ἀπὸ λεόντων τὴν μονογενῆ μου.
Lord, when will you take notice?
Restore my life from their wickedness,
and my monogenēs from lions.
Here יְחִידָתִֽי appears as feminine, and ‘soul’ or ‘life’ is probably to be inferred, certainly on the basis of the parallelism. Modern English versions have all taken it in this sense. It may be that the connotation of treasured, dearly-beloved, as attached to a sole child, has been fronted in the significance of yachid, and that the LXX has attempted to preserve this in its translations here.
Psalms of Solomon
Psalms of Solomon 18:4 presents an interesting text in terms of later Christian usage, as it juxtaposes πρωτότοκος and μονογενής directly.
ἡ παιδεία σου ἐφʼ ἡμᾶς ὡς υἱὸν πρωτότοκον μονογενῆ
ἀποστρέψαι ψυχὴν εὐήκοον ἀπὸ ἀμαθίας ἐν ἀγνοίᾳ. 
Your discipline is upon us as on a firstborn, an only son,
to turn back the obedient soul from ignorant stupidity.
The referent is Israel, in a familiar depiction of Israel as a nation, as God’s ‘son’, but here used figuratively as a son under discipline. That sonship is modified as both ‘firstborn’, and ‘siblingless’. These, of course, may both be true – a first born child is naturally siblingless until a second child is born. Nonetheless, the much later distinction of Athanasius and Gregory of Nyssa still holds: μονογενής refers to an absence of siblings, but πρωτότοκος is said in relation to siblings (whether they are present or not). Here the two words evoke two different conceptual and affective dimensions. For Israel as πρωτότοκος is heir, as μονογενής is cherished and delighted son.
Wisdom of Solomon 7:22
In Wisdom 7:22 we find another variant usage:
Ἔστιν γὰρ ἐν αὐτῇ πνεῦμα νοερόν, ἅγιον, μονογενές, πολυμερές, λεπτόν, εὐκίνητον, τρανόν, ἀμόλυντον, σαφές, ἀπήμαντον, φιλάγαθον, ὀξύ, 
For there is in her a spirit that is intelligent, holy, unique, of many parts, subtle, free-moving, lucid, unpolluted, distinct, invulnerable, loving the good, sharp,
This term here has the sense of ‘unique’. Given the overlap between both (a) a personification of Wisdom (the referent here), and (b) philosophical language, and that the direct referent is πνεῦμα, this sense marks an understandable departure from the general ‘siblingless’ signification in reference to persons.
There is a final reference in Odes 14.13, which is clearly a later, Christian composition and built on the development of μονογενής as a specific title for Jesus.
(13) κύριε υἱὲ μονογενὴ
(14) Ἰησοῦ Χριστὲ
Yachid when it’s not μονογενής
We should also consider, albeit briefly, the instances where yachid has been translated otherwise in the LXX. There are eight such instances, translated with three other terms in the LXX. These are Gen 22:2, 22:12, 22:16, Jer 6:26, Amos 8:10, and Zech 12:10 where yachid is rendered with ἀγαπητός. Proverbs 4:3 has ἀγαπώμενος, virtually equivalent in meaning. LXX Ps 67:7 has μονοτρόπους, referring to those that are alone/lonely. The preponderance of the choice of ἀγαπητός suggests that the connotation of dearly beloved associated with an only child is the fore-grounded element for LXX translations of yachid. This is suggestive, though not determinative, for a consideration of the New Testament corpus.
 Odes 14.13.
 Judges 11.34, Codex Alexandrinus. Vaticanus differs slightly but not materially:
καὶ ἦν αὕτη μονογενής, οὐκ ἦν αὐτῷ ἕτερος υἱὸς ἢ θυγάτηρ.
 Biblia Hebraica Stuttgartensia : With Westminster Hebrew Morphology., electronic ed. (Stuttgart; Glenside PA: German Bible Society; Westminster Seminary, 1996), Jdg 11:34.
 Tobias 3.15 […] μονογενής εἰμι τῷ πατρί μου, καὶ οὐχ ὑπάρχει αὐτῷ παιδίον, ὃ κληρονομήσει αὐτόν, οὐδὲ ἀδελφὸς ἐγγὺς οὐδὲ ὑπάρχων αὐτῷ υἱός, ἵνα συντηρήσω ἐμαυτὴν αὐτῷ γυναῖκα.
 Tobias 6.11 εἶπεν ὁ ἄγγελος τῷ παιδαρίῳ Ἄδελφε, σήμερον αὐλισθησόμεθα παρὰ Ραγουηλ, καὶ αὐτὸς συγγενής σού ἐστιν, καὶ ἔστιν αὐτῷ θυγάτηρ μονογενὴς ὀνόματι Σαρρα,
 Tobias 8.17 εὐλογητὸς εἶ ὅτι ἠλέησας δύο μονογενεῖς, ποίησον αὐτοῖς, δέσποτα, ἔλεος, συντέλεσον τὴν ζωὴν αὐτῶν ἐν ὑγιείᾳ μετὰ εὐφροσύνης καὶ ἐλέους.
 Throughout I provide first the LXX reference, then the MT reference in brackets.
 NETS translation.
 See Athanasius, Contra Arianos 2.62, Gregory of Nyssa, De Perfectione, Jaeger (ed), 200-1.
 NETS translation
 MT 68:7, EVV 68:6.
 If anything, it may suggest more about the description in the synoptics of Jesus as ὁ υἱός μου ὁ ἀγαπητός as in Matt 3:17 and similar. Namely, that the synoptic references to Jesus as ὁ ἀγαπητός are their equivalents to John’s ὁ μονογενής.