Only getting 6-20 fps on minecraft on high end gaming computer?

The specs are
ASUS GeForce 770 DirectCU II OC with 2GB of vRam and the latest bios
WD Caviar Black 1tb 7200RPM HDD I believe that's the speed but I can't be certain
1 3TB Seagate HDD
16GB Corsair Vengance 1600mhz
Corsair H80i liquid CPU cooler
Rosewill Lightning 800W Gold power supply
And before anyone asks, yes the fan filters on the case are clean.

Added (1). It is probably worth mentioning that the game IS heavily modded and that this only happens in one chunk. Otherwise my FPS is closer to 120.

Added (2). Another update, forgot the CPU Intel i7 4770k quad core

Added (3). Really wish there was a way to edit these without having to do an update, but here
Intel i7 4770k CPU @ 3.50GHz

Added (4). To all the people who are going to tell me I need to dedicate more ram to minecraft, I already have 6 gigs dedicated

Added (5). And it's a frame rate issue, not a ram/ crashing issue.

There's one Spec you are leaving out of your list (or i just failed to se it) but Minecraft is a ssingle-threaded game which means it only runs on 1-core of your cpu, if your cpu, like mine, is low 2.5 ghz or so it will seem to run slow. I would try usiing a mod that can improve it - OptiFine helps with improing Fps lag

Did you install all of the latest drivers for your GPU?