Psalms 111-112 are a response to Psalm 110, according to The Composition and Theology of the Fifth Book of Psalms, Psalms 107-145 [sic] by Eric Zenger, Journal for the Study of the Old Testament 1998; 23; 77.
I have adjusted my table of contents slightly to reflect some of his statements - notably the chaistic relationship of the Songs of Ascent. It appears that I will need to make the details more visible - hopefully later. - Here's a sample of his structural ideas.
Psalm 111 celebrates [the LORD]’s turning towards his people in rescue. Psalm 112 extols an ['ish]~ whose actions correspond to [the LORD] praised in Psalm 111. The composition directs the reader to see in the ['ish] of Psalm 112 the king whom [the LORD] has called to his side in Psalm 110. [see also Psalm 1].Eventually I will follow up some of these claims with an image. To be convinced of a structural feature, I think I need some confirming aspect in the poem or some uniqueness in the set of poems. Book 5 does have some complexity that needs a visual aid.
(2) Psalms 111 and 112 are connected to Psalms 108-10 by the theme of [rsh']- of this I am not yet convinced [rsh' appears only in psalm 109 as a structural element and in psalm 112 once] - which is missing in Psalms 113-18 (and in Pss. 120-37 with the exception of 129.4).
(3) Each of the two acrostics 111-12 shares with the acrostic Psalm 145 the citation of the Sinai-formula, Exod. 34.6 (111.4 and 112.4 have the same word order as 145.8, namely, [xnun vraxum]).