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At many exchanges the opening price is set using an auction which takes place pre-opening (see here for example). During the auction you are allowed to place orders according to certain rules (you might for example be prevented to cancel any order you have made).

Do you know of any established models or "rule of thumb" for predicting at what order volume you would move the opening price?

If you place an order larger than the current bid/ask volume you would probably move the opening price, but the problem is made harder (I think at least!) since there are also hidden order volumes.

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We can't really just give-out trading strategies here. Is there something more specific you were looking for? Have you done prior research in this topic? –  chrisaycock Jun 17 '13 at 15:11
    
I don't even understand the question. Do you mean how to measure the price impact of an order at the opening, conditional on its size? What is you reference price? –  Robert Kubrick Jun 17 '13 at 16:22
    
I agree with Robert, I do not understand the question. Please rephrase. –  Matt Wolf Jun 17 '13 at 22:33
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The simplest rule of thumb I could think of is any volume greater than the current bid/ask volume? This would apply to any time of day and is perhaps a too simple answer –  Filip Jun 18 '13 at 8:03
    
Sorry, I'll clarify the question above. –  user2078515 Jun 18 '13 at 9:35

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I am not aware about any rule of thumb on market impact during fixing auctions (nothing comparable with the usual square root rule for meta orders market impact). In Navigating Liquidity 6 - A global menu for optimal trading, there is a study about the liquidity during the fixing auctions, you should start from here.

Another important point is the data you have access to to fit your model.

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