You might be able to recover the file but its imperative that you stop using the Mac! If you keep using it its likely the file will be overridden by newer files.
Software such as Data Rescue or Disk Drill may be able to recover the file. Keep in mind that if the drive has physical problems this is unlikely to work!
This is how it will work:
1. You boot the Mac from the external drive that contains the software. Very important, using it from the internal drive is very bad idea because it risk overriding the file you are trying to recover!
2. Open the software and point it to internal drive, you will also need a second drive for temporary work space.
3. The software shows you what it can recover, select the file if its on the list and press recover, software saves the file on the external drive. Open the drive and try opening the file, if its correct file you can copy it to another drive for safekeeping and your done. If you need more files you have to purchase the software, they will usually only allow you to recover one file without payment.
If the software can't recover the file then you could try another software but there is no quarantine of success. Professional assistance is more likely to succeed but it could be expensive.