PC GAMESS/Firefly-related discussion club

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sanya
sanya@photonics.ru

>>1. What was the geometry to compute T1/S0 SO coupling?
>  I used mainly S0 geometry, in some cases averaged one of S0 and T1 computed
> from ALDET option of MCSCF.

I'm afraid there is some misunderstanding.

The wavefunction of a molecule depends on the electron and nuclear coordinates. According to Born-Oppenheimer approximation, this wavefunction can be (appoximately) broken into its electronic (depending on the electron coordinates) and nuclear (depending on nuclear coordinates) components. When you obtain an electron wavefunction of a certain state (say, by SCF procedure), you deal with electron coordinates. When you optimize the geometry of a certain electronic state of a molecule, you minimize the energy of your molecule (in this state) with respect to the nuclear coordinates. The energy of the molecule in a given state as a function of nuclear coordinates is called potential energy surface of this state.

A potential energy surface of a given state can have a minimum (probably, several minima) called equilibrium geometry of this state or have no minima at all. Each nuclear configuration corresponds to some point on the potential energy surface of a state. Say, the saddle point of the ground state (S0) potential energy surface can correspond to the minimum on the S1 excited state potential energy surface and vice versa.

Therefore, your molecular geometry averaged  of S0 and T1 corresponds to some arbitrary point on both S0 and T1 surfaces. In this sense, it is meaningless, because it is neither the equilibrium geometry of S0 nor the equilibrium geometry of T1. It is just a point.

When using the S0 equilibrium geometry, you obtain the SO value for the ground state (spin-orbit coupling between S0 and T1 in the ground state equilibrium geometry). When using T1 equilibrium geometry, you get this value for T1 (spin-orbit coupling between S0 and T1 in the T1 state equilibrium geometry). When using any arbitrary geometry (say, your averaged geometry of S0 and T1, which can correspond to a point somewhere between S0 and T1 minima), you obtain the property for this point. If this is not a special point, the SO value for it is not interesting as such. However, you may present SO values along some curve (it is expected that the curve is not an arbitrary curve but is interesting in some aspect) or across a grid.

The above three paragraphs are all about nuclear coordinates. When speaking about wavefunction and orbitals, we mean electron coordinates. State-averaged orbitals are not as meaningless as "state-averaged geometry". These orbitals can be a good starting point for some next-level calculations. However, they should never be used for data interpretation. I mean that any molecular properties should be discussed in terms of state-specific orbitals or no orbitals at all (one should try to use other terms if only state-averaged orbitals are available).

>>Was it the equilibrium geometry of T0? of S0? some other geometry?
>  I do not always confirm whether the obtained geometry is the equilibrium
> geometry or not, since the vibrational analysis is often time consuming.

Geometry optimization ends when the energy gradient with respect to nuclear coordinates becomes zero. In fact, this is a stationary point on the potential energy surface, but we may hope that this is a real minimum. To be sure of this, you may perform vibrational analysis. For medium-size molecules it is not very time-consuming.