Current-to-voltager amplifier (TIA): dual vs. single supply OpAmp

[Bigman]

Hi,
in the attachment "TIA_dial_supply" you see my first circuit for a transimpedance amplifier. In this circuit the reference voltage at the non-inverting input is just in between the negativ and postive supply voltage of the OpAmp. To get this reference voltage, the circuit compromises a rail-splitter.

Then, I heard about Input Common-Mode Voltage range, and I was wondering: if an OpAmp even accepts voltages below his negative supply voltage, I may not need the rail-splitter anymore.
So, I came up with the circuit "TIA_single_supply". The difference to the 1st circuit: the non-inverting input and the negative supply voltage are now connected with GND.

But according to the simulations, this is not working. Interestingly, the Output-voltage is even lower than the input voltage in case of the single supply.
(The choosen OpAmp has an Input Common-Mode Voltage range of V- - 0.2V, and V+ + 0.2V.)

Perhaps somebody can give me a hint, where my thinking is wrong.
Thanks!

[TimFox]

In your second circuit as drawn, with the input current (with zero DC component) to the inverting input and a feedback resistor from output to inverting input, an ideal op-amp (ignoring power supply issues) would have an output that swings positive and negative from ground, to balance the input current through the feedback resistor.  Even though the input common-mode range goes below the negative power supply pin (which you have grounded), the output cannot swing negative with respect to the negative power supply = ground.
If you want to see the variation on the input, you need to connect the non-inverting input to an intermediate positive voltage, or add negative current (resistor from a supply negative to ground) to bias the output positive (between the two supply pins).