I note that the data you are interested are in the last part of the file. The reverse <$fh> is a pretty clunky way to read the file backwards but it works. If you can install File::ReadBackwards, it will be nicer, I think.

A slightly nicer version of your program:

foreach my $f (<*log>){
    open my $fh,'<',$f;
    my @lines = reverse <$fh>;
    close $fh;
    next if ((shift @lines) !~ /Normal termination/);
    
    # Find the bond length. We assume this is built into the file name
+ 
    my $R = $f;
    $R=~s/.log//;
    $R=~s/.*_//;
    my ($u,$edra,$edrb,@EDRvars,@Uvars);
    foreach my $line (@lines) {
      next unless ($line =~ m/^   \d/);
      last if ($line =~ m/^  Index/);
      (undef,undef,$u,$edra,$edrb) = unpack('A7A17A17A17A17',$line);
      push @Uvars, $u;
      push @EDRvars, $edra + $edrb;
    }
    # Print the outputs 
    foreach my $i(0..$#Uvars){
        print sprintf("%8.3E %12.6E %12.6E\n",$R,$Uvars[$i],$EDRvars[$
+i]);
    }        
}
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