I'm no expert, but looking at this reminds me of a problem I had with benzene. There's a totally unscientific pattern here that might help you remember the correct molecular orbitals. I only learned this from looking at your molecular system here, so I don't know how well it extends to other systems (it might!)
First, examine the chain as a ring (this is what I did for Benzene). If you imagine your proposed molecular orbital arrays as wrapping around like in a cyclic molecule, you'd see they're actually equivalent to the correct molecular orbital representations. At that point, it's a question of determining which equivalent representation is the correct one. The rule of thumb here is that the correct arrangement:
- Maintains appropriate symmetry.
Appropriate symmetry refers to odd-numbered molecular orbitals having a vertical axis of reflection down the center of the array, while even-numbered molecular orbitals possess a center of inversion.
- Maximizes the number of pairs of one type, a type being either a "same-sign" pairing of molecular orbitals or an "opposite-sign" pairing.
Using your example:
Psi-3: Your proposed array, from left to right, follows a pattern of "opposite-sign" pair, "same-sign" pair, "opposite-sign" pair, whereas the correct arrangement features 3 "same-sign" pairs. The correct arrangement takes precedence because it maximizes the number of pairs of a single type, having 3 pairs of one type as opposed to yours only having 2 pairs of one type.
Psi-4: Similar to the previous example, from left to right, the correct arrangement has 3 "opposite-sign" pairs. Yours has at most two pairs of one type (2 "same-sign" pairs in your case)
Psi-5: In the psi-5 case, an alternative array with superior pairing doesn't exist, but an arrangement with equivalent pairing does; however, this latter array would sacrifice the appropriate symmetry and is therefore not correct.
I just came up with this trick here on the spot, so I don't know how consistently this it works (and physically I'm sure it's terribly wrong). It does seem to work with smaller even-number systems, but it has trouble dealing with nodes in larger even-systems like octatetraene. The pattern may otherwise be generalizable to smaller even-number-electron conjugated pi systems.
Where this pattern fails
The pattern starts to break down when you examine odd-number-center systems and large even-center systems with nodes (like psi 3 and 6 in octatetraene). With some modifications, the pattern can still work, albeit perhaps becoming too complicated for practical use. Also none of it applies to conjugated cyclic systems which have degenerate orbitals.
For odd-number systems and even-system with nodes (psi 3/6 in octatetraene), counting the interactions between adjacent orbitals becomes necessary. For example, in pentadienyl radical/ion, my pattern would suggest the psi-3 orbital as down/up/up/up/down, but the correct answer is down/node/up/node/down. Counting adjacent like-sign orbitals as +1 and nodes as zero, this only makes sense if adjacent opposite-sign orbitals are valued at slightly less than -1. The sum of the orbital interaction then favors the system with nodes. This applies in even-systems as well, such as comparing the presence of nodes in psi-3 (up/up/node/down/down/node/up/up) of octatetraene to an alternative up/up/down/down/down/down/up/up array (which is a rearrangement of psi-2, similar to how butadiene's psi-3 compares to its psi-2 -- my pattern works there). Kind of complicated then I guess.