  We present a combined experimental and theoretical study on the
quasi-one-dimensional organic conductor (TMTTF)$_2$PF$_6$, and elucidate the
variation of its physical properties under pressure. We fully resolve the
crystal structure by single crystal x-ray diffraction measurements using a
diamond anvil cell up to 8 GPa, and based on the structural data, we perform
first-principles density-functional theory calculations and derive the $ab$
$initio$ extended Hubbard-type Hamiltonians. Furthermore, we compare the
behavior of the resistivity measured up to 3 GPa using a BeCu clamp-type cell
and the ground state properties of the obtained model numerically calculated by
the many-variable variational Monte Carlo method. Our main findings are as
follows: i) The crystal was rapidly compressed up to about 3 GPa where the
volume drops to 80% and gradually varies down to 70% at 8 GPa. The transfer
integrals increase following such behavior whereas the screened Coulomb
interactions decrease, resulting in a drastic reduction of correlation effect.
ii) The degree of dimerization in the intrachain transfer integrals, as the
result of the decrease in structural dimerization together with the change in
the intermolecular configuration, almost disappears above 4 GPa; the interchain
transfer integrals also show characteristic variations under pressure. iii) The
results of identifying the characteristic temperatures in the resistivity and
the charge and spin orderings in the calculations show an overall agreement:
The charge ordering sensitively becomes unstable above 1 GPa, while the spin
ordering survives up to higher pressures. These results shed light on the
similarities and differences between applying external pressure and
substituting the chemical species (chemical pressure).
