Difference in calculated pH and the real pH of a phosphate buffer

I want to prepare a buffer system with $$\mathrm{pH} = 7.00$$ and a total concentration $$c_\mathrm{tot} = \pu{0.10 mol l^-1}$$ using sodium hydrogen phosphate $$(\ce{Na2HPO4})$$ and sodium dihydrogen phosphate $$(\ce{NaH2PO4})$$ salts. I am calculating the amounts to prepare a phosphate buffer as follows:

$$\ce{H2PO4- <=> HPO4^2- + H+} \qquad \mathrm{p}K_\mathrm{a} = 7.20 \tag{R1}$$

$$\mathrm{pH} = \mathrm{p}K_\mathrm{a} + \log\frac{[\ce{HPO4^2-}]}{[\ce{H2PO4-}]} \tag{1}$$

$$\frac{[\ce{HPO4^2-}]}{[\ce{H2PO4-}]} = 10^{\mathrm{pH} - \mathrm{p}K_\mathrm{a}} = 10^{7.00-7.20} \approx 0.632 \tag{2}$$

\begin{align} c_\mathrm{tot} &= [\ce{H2PO4-}] + [\ce{HPO4^2-}] \\ &= [\ce{H2PO4-}] + [\ce{H2PO4-}]\times 0.632 \\ &= [\ce{H2PO4-}]\times 1.632 \tag{3} \end{align}

$$[\ce{H2PO4-}] = \frac{c_\mathrm{tot}}{1.632} = \frac{\pu{0.10 mol l^-1}}{1.632} \approx \pu{0.061 mol l^-1}\tag{4}$$

$$[\ce{HPO4^2-}] = c_\mathrm{tot} - [\ce{H2PO4-}] = \pu{0.10 mol l^-1} - \pu{0.061 mol l^-1} = \pu{0.039 mol l^-1} \tag{5}$$

For the preparation of $$V = \pu{500 ml}$$ buffer solution I used the following masses of corresponding salts:

\begin{align} m(\ce{NaH2PO4}) &= [\ce{H2PO4-}]\cdot V\cdot M(\ce{NaH2PO4}) \\ &= (\pu{0.061 mol l^-1})(\pu{0.500 l})(\pu{119.97 g mol^-1}) \\ &\approx\pu{3.66 g} \tag{6} \end{align}

\begin{align} m(\ce{Na2HPO4}) &= [\ce{HPO4^2-}]\cdot V\cdot M(\ce{Na2HPO4}) \\ &= (\pu{0.039 mol l^-1})(\pu{0.500 l})(\pu{141.97 g mol^-1}) \\ &\approx\pu{2.77 g} \tag{7} \end{align}

When I mixed the calculated amounts, the obtained $$\mathrm{pH} = 6.5$$ deviated quite a lot from the desired value. I thought it was my mistake in calculations or an error when I weighed the amounts, but I repeated everything several times and still not get the $$\mathrm{pH} = 7.00,$$ and the value always was $$6.4$$ or $$6.5.$$

I would like to know the reason. I think if the concentration of the monobasic salt is greater than the one of the dibasic salt, the $$\mathrm{pH}$$ tends to decrease, but in the calculations the relation [dibasic]/[monobasic] is always less than 1 and this again causes [monobasic] > [dibasic].

The flaw in your calculations is the assumption that the $$\mathrm{p}K_\mathrm{a}$$ is a constant independent of concentration. In reality, $$\mathrm{p}K_\mathrm{a}$$ is a function of the ionic strength $$I$$.
At infinite dilution $$I = 0$$ and $$\mathrm{p}K_\mathrm{a} = 7.20$$ as you assumed. However at the concentration $$\pu{0.10 mol l^-1}$$ of phosphate buffer $$\mathrm{p}K_\mathrm{a} = 6.81.$$ See Florida State University — Phosphate Buffers and the paper by Green [1].