  We successfully synthesized the zinc-verdazyl complex
[Zn(hfac)$_2$]$\cdot$($o$-Py-V) [hfac = 1,1,1,5,5,5-hexafluoroacetylacetonate;
$o$-Py-V = 3-(2-pyridyl)-1,5-diphenylverdazyl], which is an ideal model
compound with an $S$ = 1/2 ferromagnetic-antiferromagnetic alternating
Heisenberg chain (F-AF AHC). $Ab$ $initio$ molecular orbital (MO) calculations
indicate that two dominant interactions $J_{\rm{F}}$ and $J_{\rm{AF}}$ form the
$S=1/2$ F-AF AHC in this compound. The magnetic susceptibility and magnetic
specific heat of the compound exhibit thermally activated behavior below
approximately 1 K. Furthermore, its magnetization curve is observed up to the
saturation field and directly indicates a zero-field excitation gap of 0.5 T.
These experimental results provide evidence for the existence of a Haldane gap.
We successfully explain the results in terms of the $S=1/2$ F-AF AHC through
quantum Monte Carlo calculations with $|J_{\rm{AF}}/J_{\rm{F}}|$ = 0.22. The
$ab$ $initio$ MO calculations also indicate a weak AF interchain interaction
$J'$ and that the coupled F-AF AHCs form a honeycomb lattice. The $J'$
dependence of the Haldane gap is calculated, and the actual value of $J'$ is
determined to be less than 0.01$|J_{\rm{F}}|$.
