You need two passes to do ($5 - minimum of 5th column)*627.509
for each row
Try this:
awk 'NR==FNR{min=min<$5?min:$5;next}{$5=($5-min)*627.509}1' OFS='\t' file file
$ cat file
SCFE: SCF energy: UDFT(b3lyp) -7255.77607552893 hartrees iterations: 36
SCFE: SCF energy: UDFT(b3lyp) -7256.47180169446 hartrees iterations: 13
SCFE: SCF energy: UDFT(b3lyp) -7257.05043442327 hartrees iterations: 25
SCFE: SCF energy: UDFT(b3lyp) -7257.53756596970 hartrees iterations: 7
SCFE: SCF energy: UDFT(b3lyp) -7257.94483191615 hartrees iterations: 7
SCFE: SCF energy: UDFT(b3lyp) -7258.28358389906 hartrees iterations: 7
SCFE: SCF energy: UDFT(b3lyp) -7258.56278138629 hartrees iterations: 7
$ awk 'NR==FNR{min=min<$5?min:$5;next}{$5=($5-min)*627.509}1' OFS='\t' file file
SCFE: SCF energy: UDFT(b3lyp) 1748.68 hartrees iterations: 36
SCFE: SCF energy: UDFT(b3lyp) 1312.11 hartrees iterations: 13
SCFE: SCF energy: UDFT(b3lyp) 949.011 hartrees iterations: 25
SCFE: SCF energy: UDFT(b3lyp) 643.332 hartrees iterations: 7
SCFE: SCF energy: UDFT(b3lyp) 387.769 hartrees iterations: 7
SCFE: SCF energy: UDFT(b3lyp) 175.199 hartrees iterations: 7
SCFE: SCF energy: UDFT(b3lyp) 0 hartrees iterations: 7